Given the following C code and assembly code, your task is to generate highly optimized x86-64 assembly code.
C Code:

```c
N;M;i;j;r;main(K){for(scanf("%d%d%d",&N,&M,&K);i<N;++i)for(j=0;j<=M;++j)r+=i*j+(N-i)*(M-j)==K;puts(r?"Yes":"No");}```

Assembly Code:

```assembly
	.file	"temp.c"
	.text
	.section	.rodata.str1.1,"aMS",@progbits,1
.LC1:
	.string	"Yes"
.LC2:
	.string	"No"
.LC3:
	.string	"%d%d%d"
	.section	.text.startup,"ax",@progbits
	.p2align 4
	.globl	main
	.type	main, @function
main:
.LFB0:
	.cfi_startproc
	endbr64
	pushq	%r14
	.cfi_def_cfa_offset 16
	.cfi_offset 14, -16
	leaq	M(%rip), %rdx
	leaq	N(%rip), %rsi
	xorl	%eax, %eax
	pushq	%r13
	.cfi_def_cfa_offset 24
	.cfi_offset 13, -24
	pushq	%r12
	.cfi_def_cfa_offset 32
	.cfi_offset 12, -32
	pushq	%rbp
	.cfi_def_cfa_offset 40
	.cfi_offset 6, -40
	pushq	%rbx
	.cfi_def_cfa_offset 48
	.cfi_offset 3, -48
	subq	$16, %rsp
	.cfi_def_cfa_offset 64
	movl	%edi, 12(%rsp)
	leaq	12(%rsp), %rcx
	leaq	.LC3(%rip), %rdi
	call	scanf@PLT
	movl	i(%rip), %edx
	movl	N(%rip), %ebx
	cmpl	%ebx, %edx
	jge	.L3
	movl	M(%rip), %esi
	movl	12(%rsp), %r11d
	xorl	%eax, %eax
	movdqa	.LC4(%rip), %xmm8
	movl	r(%rip), %ecx
	leal	1(%rsi), %ebp
	movd	%esi, %xmm4
	movd	%r11d, %xmm5
	movl	%ebp, %r8d
	movl	%ebp, %r12d
	pshufd	$0, %xmm4, %xmm10
	shrl	$2, %r8d
	andl	$-4, %r12d
	pshufd	$0, %xmm5, %xmm9
	.p2align 4,,10
	.p2align 3
.L9:
	testl	%esi, %esi
	js	.L12
	movl	%ebx, %r9d
	subl	%edx, %r9d
	cmpl	$4, %esi
	jbe	.L13
	movd	%edx, %xmm4
	movd	%r9d, %xmm5
	pxor	%xmm2, %xmm2
	xorl	%eax, %eax
	pshufd	$0, %xmm4, %xmm4
	pshufd	$0, %xmm5, %xmm5
	movdqa	.LC0(%rip), %xmm3
	movdqa	%xmm5, %xmm7
	movdqa	%xmm4, %xmm6
	psrlq	$32, %xmm7
	psrlq	$32, %xmm6
	.p2align 4,,10
	.p2align 3
.L6:
	movdqa	%xmm3, %xmm0
	movdqa	%xmm10, %xmm1
	addl	$1, %eax
	psubd	%xmm0, %xmm1
	paddd	%xmm8, %xmm3
	movdqa	%xmm1, %xmm11
	psrlq	$32, %xmm1
	pmuludq	%xmm5, %xmm11
	pmuludq	%xmm7, %xmm1
	pshufd	$8, %xmm11, %xmm11
	pshufd	$8, %xmm1, %xmm1
	punpckldq	%xmm1, %xmm11
	movdqa	%xmm0, %xmm1
	psrlq	$32, %xmm0
	pmuludq	%xmm4, %xmm1
	pmuludq	%xmm6, %xmm0
	pshufd	$8, %xmm1, %xmm1
	pshufd	$8, %xmm0, %xmm0
	punpckldq	%xmm0, %xmm1
	movdqa	%xmm11, %xmm0
	paddd	%xmm1, %xmm0
	pcmpeqd	%xmm9, %xmm0
	psubd	%xmm0, %xmm2
	cmpl	%r8d, %eax
	jne	.L6
	movdqa	%xmm2, %xmm0
	movl	%r12d, %edi
	psrldq	$8, %xmm0
	paddd	%xmm0, %xmm2
	movdqa	%xmm2, %xmm0
	psrldq	$4, %xmm0
	paddd	%xmm0, %xmm2
	movd	%xmm2, %eax
	addl	%eax, %ecx
	cmpl	%ebp, %r12d
	je	.L8
.L5:
	movl	%esi, %r10d
	movl	%edx, %r13d
	xorl	%eax, %eax
	subl	%edi, %r10d
	imull	%edi, %r13d
	imull	%r9d, %r10d
	addl	%r13d, %r10d
	cmpl	%r11d, %r10d
	sete	%al
	addl	%eax, %ecx
	leal	1(%rdi), %eax
	cmpl	%eax, %esi
	jl	.L8
	movl	%esi, %r10d
	addl	%edx, %r13d
	leal	2(%rdi), %r14d
	subl	%eax, %r10d
	xorl	%eax, %eax
	imull	%r9d, %r10d
	addl	%r13d, %r10d
	cmpl	%r11d, %r10d
	sete	%al
	addl	%eax, %ecx
	cmpl	%r14d, %esi
	jl	.L8
	movl	%esi, %r10d
	addl	%edx, %r13d
	xorl	%eax, %eax
	subl	%r14d, %r10d
	leal	3(%rdi), %r14d
	imull	%r9d, %r10d
	addl	%r13d, %r10d
	cmpl	%r11d, %r10d
	sete	%al
	addl	%eax, %ecx
	cmpl	%r14d, %esi
	jl	.L8
	movl	%esi, %r10d
	leal	(%rdx,%r13), %eax
	subl	%r14d, %r10d
	imull	%r9d, %r10d
	addl	%eax, %r10d
	cmpl	%r11d, %r10d
	sete	%r10b
	addl	$4, %edi
	movzbl	%r10b, %r10d
	addl	%r10d, %ecx
	cmpl	%edi, %esi
	jl	.L8
	movl	%esi, %r10d
	addl	%edx, %eax
	subl	%edi, %r10d
	movl	%r10d, %edi
	imull	%r9d, %edi
	addl	%edi, %eax
	cmpl	%r11d, %eax
	sete	%al
	movzbl	%al, %eax
	addl	%eax, %ecx
.L8:
	movl	%ebp, %edi
	movl	$1, %eax
.L4:
	addl	$1, %edx
	cmpl	%ebx, %edx
	jne	.L9
	movl	%edi, j(%rip)
	movl	%edx, i(%rip)
	testb	%al, %al
	je	.L3
	movl	%ecx, r(%rip)
.L3:
	movl	r(%rip), %eax
	leaq	.LC1(%rip), %rdi
	testl	%eax, %eax
	leaq	.LC2(%rip), %rax
	cmove	%rax, %rdi
	call	puts@PLT
	addq	$16, %rsp
	.cfi_remember_state
	.cfi_def_cfa_offset 48
	xorl	%eax, %eax
	popq	%rbx
	.cfi_def_cfa_offset 40
	popq	%rbp
	.cfi_def_cfa_offset 32
	popq	%r12
	.cfi_def_cfa_offset 24
	popq	%r13
	.cfi_def_cfa_offset 16
	popq	%r14
	.cfi_def_cfa_offset 8
	ret
	.p2align 4,,10
	.p2align 3
.L12:
	.cfi_restore_state
	xorl	%edi, %edi
	jmp	.L4
.L13:
	xorl	%edi, %edi
	jmp	.L5
	.cfi_endproc
.LFE0:
	.size	main, .-main
	.globl	r
	.bss
	.align 4
	.type	r, @object
	.size	r, 4
r:
	.zero	4
	.globl	j
	.align 4
	.type	j, @object
	.size	j, 4
j:
	.zero	4
	.globl	i
	.align 4
	.type	i, @object
	.size	i, 4
i:
	.zero	4
	.globl	M
	.align 4
	.type	M, @object
	.size	M, 4
M:
	.zero	4
	.globl	N
	.align 4
	.type	N, @object
	.size	N, 4
N:
	.zero	4
	.section	.rodata.cst16,"aM",@progbits,16
	.align 16
.LC0:
	.long	0
	.long	1
	.long	2
	.long	3
	.align 16
.LC4:
	.long	4
	.long	4
	.long	4
	.long	4
	.ident	"GCC: (Ubuntu 11.4.0-1ubuntu1~22.04) 11.4.0"
	.section	.note.GNU-stack,"",@progbits
	.section	.note.gnu.property,"a"
	.align 8
	.long	1f - 0f
	.long	4f - 1f
	.long	5
0:
	.string	"GNU"
1:
	.align 8
	.long	0xc0000002
	.long	3f - 2f
2:
	.long	0x3
3:
	.align 8
4:
```

Only output the optimized assembly code. Do not include any other text. Do not write any comments in the assembly code. Wrap the assembly code in ```assembly``` tags.
Optimized Assembly Code:

user
```assembly
	.file	"temp.c"
	.text
	.section	.rodata.str1.1,"aMS",@progbits,1
.LC1:
	.string	"Yes"
.LC2:
	.string	"No"
.LC3:
	.string	"%d%d%d"
	.section	.text.startup,"ax",@progbits
	.p2align 4
	.globl	main
	.type	main, @function
main:
.LFB0:
	.cfi_startproc
	endbr64
	pushq	%r14
	.cfi_def_cfa_offset 16
	.cfi_offset 14, -16
	leaq	M(%rip), %rdx
	leaq	N(%rip), %rsi
	xorl	%eax, %eax
	pushq	%r13
	.cfi_def_cfa_offset 24
	.cfi_offset 13, -24
	pushq	%r12
	.cfi_def_cfa_offset 32
	.cfi_offset 12, -32
	pushq	%rbp
	.cfi_def_cfa_offset 40
	.cfi_offset 6, -40
	pushq	%rbx
	.cfi_def_cfa_offset 48
	.cfi_offset 3, -48
	subq	$16, %rsp
	.cfi_def_cfa_offset 64
	movl	%edi, 12(%rsp)
	leaq	12(%rsp), %rcx
	leaq	.LC3(%rip), %rdi
	call	scanf@PLT
	movl	i(%rip), %edx
	movl	N(%rip), %ebx
	cmpl	%ebx, %edx
	jge	.L3
	movl	M(%rip), %esi
	movl	12(%rsp), %r11d
	xorl	%eax, %eax
	movdqa	.LC4(%rip), %xmm8
	movl	r(%rip), %ecx
	leal	1(%rsi), %ebp
	movd	%esi, %xmm4
	movd	%r11d, %xmm5
	movl	%ebp, %r8d
	movl	%ebp, %r12d
	pshufd	$0, %xmm4, %xmm10
	shrl	$2, %r8d
	andl	$-4, %r12d
	pshufd	$0, %xmm5, %xmm9
	.p2align 4,,10
	.p2align 3
.L9:
	testl	%esi, %esi
	js	.L12
	movl	%ebx, %r9d
	subl	%edx, %r9d
	cmpl	$4, %esi
	jbe	.L13
	movd	%edx, %xmm4
	movd	%r9d, %xmm5
	pxor	%xmm2, %xmm2
	xorl	%eax, %eax
	pshufd	$0, %xmm4, %xmm4
	pshufd	$0, %xmm5, %xmm5
	movdqa	.LC0(%rip), %xmm3
	movdqa	%xmm5, %xmm7
	movdqa	%xmm4, %xmm6
	psrlq	$32, %xmm7
	psrlq	$32, %xmm6
	.p2align 4,,10
	.p2align 3
.L6:
	movdqa	%xmm3, %xmm0
	movdqa	%xmm10, %xmm1
	addl	$1, %eax
	psubd	%xmm0, %xmm1
	paddd	%xmm8, %xmm3
	movdqa	%xmm1, %xmm11
	psrlq	$32, %xmm1
	pmuludq	%xmm5, %xmm11
	pmuludq	%xmm7, %xmm1
	pshufd	$8, %xmm11, %xmm11
	pshufd	$8, %xmm1, %xmm1
	punpckldq	%xmm1, %xmm11
	movdqa	%xmm0, %xmm1
	psrlq	$32, %xmm0
	pmuludq	%xmm4, %xmm1
	pmuludq	%xmm6, %xmm0
	pshufd	$8, %xmm1, %xmm1
	pshufd	$8, %xmm0, %xmm0
	punpckldq	%xmm0, %xmm1
	movdqa	%xmm11, %xmm0
	paddd	%xmm1, %xmm0
	pcmpeqd	%xmm9, %xmm0
	psubd	%xmm0, %xmm2
	cmpl	%r8d, %eax
	jne	.L6
	movdqa	%xmm2, %xmm0
	movl	%r12d, %edi
	psrldq	$8, %xmm0
	paddd	%xmm0, %xmm2
	movdqa	%xmm2, %xmm0
	psrldq	$4, %xmm0
	paddd	%xmm0, %xmm2
	movd	%xmm2, %eax
	addl	%eax, %ecx
	cmpl	%ebp, %r12d
	je	.L8
.L5:
	movl	%esi, %r10d
	movl	%edx, %r13d
	xorl	%eax, %eax
	subl	%edi, %r10d
	imull	%edi, %r13d
	imull	%r9d, %r10d
	addl	%r13d, %r10d
	cmpl	%r11d, %r10d
	sete	%al
	addl	%eax, %ecx
	leal	1(%rdi), %eax
	cmpl	%eax, %esi
	jl	.L8
	movl	%esi, %r10d
	addl	%edx, %r13d
	leal	2(%rdi), %r14d
	subl	%eax, %r10d
	xorl	%eax, %eax
	imull	%r9d, %r10d
	addl	%r13d, %r10d
	cmpl	%r11d, %r10d
	sete	%al
	addl	%eax, %ecx
	cmpl	%r14d, %esi
	jl	.L8
	movl	%esi, %r10d
	addl	%edx, %r13d
	xorl	%eax, %eax
	subl	%r14d, %r10d
	leal	3(%rdi), %r14d
	imull	%r9d, %r10d
	addl	%r13d, %r10d
	cmpl	%r11d, %r10d
	sete	%al
	addl	%eax, %ecx
	cmpl	%r14d, %esi
	jl	.L8
	movl	%esi, %r10d
	leal	(%rdx,%r13), %eax
	subl	%r14d, %r10d
	imull	%r9d, %r10d
	addl	%eax, %r10d
	cmpl	%r11d, %r10d
	sete	%r10b
	addl	$4, %edi
	movzbl	%r10b, %r10d
	addl	%r10d, %ecx
	cmpl	%edi, %esi
	jl	.L8
	movl	%esi, %r10d
	addl	%edx, %eax
	subl	%edi, %r10d
	movl	%r10d, %edi
	imull	%r9d, %edi
	addl	%edi, %eax
	cmpl	%r11d, %eax
	sete	%al
	movzbl	%al, %eax
	addl	%eax, %ecx
.L8:
	movl	%ebp, %edi
	movl	$1, %eax
.L4:
	addl	$1, %edx
	cmpl	%ebx, %edx
	jne	.L9
	movl	%edi, j(%rip)
	movl	%edx, i(%rip)
	testb	%al, %al
	je	.L3
	movl	%ecx, r(%rip)
.L3:
	movl	r(%rip), %eax
	leaq	.LC1(%rip), %rdi
	testl	%eax, %eax
	leaq	.LC2(%rip), %rax
	cmove	%rax, %rdi
	call	puts@PLT
	addq	$16, %rsp
	.cfi_remember_state
	.cfi_def_cfa_offset 48
	xorl	%eax, %eax
	popq	%rbx
	.cfi_def_cfa_offset 40
	popq	%rbp
	.cfi_def_cfa_offset 32
	popq	%r12
	.cfi_def_cfa_offset 24
	popq	%r13
	.cfi_def_cfa_offset 16
	popq	%r14
	.cfi_def_cfa_offset 8
	ret
	.p2align 4,,10
	.p2align 3
.L12:
	.cfi_restore_state
	xorl	%edi, %edi
	jmp	.L4
.L13:
	xorl	%edi, %edi
	jmp	.L5
	.cfi_endproc
.LFE0:
	.size	main, .-main
	.globl	r
	.bss
	.align 4
	.type	r, @object
	.size	r, 4
r:
	.zero	4
	.globl	j
	.align 4
	.type	j, @object
	.size	j, 4
j:
	.zero	4
	.globl	i
	.align 4
	.type	i, @object
	.size	i, 4
i:
	.zero	4
	.globl	M
	.align 4
	.type	M, @object
	.size	M, 4
M:
	.zero	4
	.globl	N
	.align 4
	.type	N, @object
	.size	N, 4
N:
	.zero	4
	.section	.rodata.cst16,"aM",@progbits,16
	.align 16
.LC0:
	.long	0
	.long	1
	.long	2
	.long	3
	.align 16
.LC4:
	.long	4
	.long	4
	.long	4
	.long	4
	.ident	"GCC: (Ubuntu 11.4.0-1ubuntu1~22.04) 11.4.0"
	.section	.note.GNU-stack,"",@progbits
	.section	.note.gnu.property,"a"
	.align 8
	.long	1f - 0f
	.long	4f - 1f
	.long	5
0:
	.string	"GNU"
1:
	.align 8
	.long	0xc0000002
	.long	3f - 2f
2:
	.long	0x3
3:
	.align 8
4:
```
rule
```assembly
	.file	"temp.c"
	.text
	.section	.rodata.str1.1,"aMS",@progbits,1
.LC1:
	.string	"Yes"
.LC2:
	.string	"No"
.LC3:
	.string	"%d%d%d"
	.section	.text.startup,"ax",@progbits
	.p2align 4
	.globl	main
	.type	main, @function
main:
.LFB0:
	.cfi_startproc
	endbr64
	pushq	%r14
	.cfi_def_cfa_offset 16
	.cfi_offset 14, -16
	leaq	M(%rip), %rdx
	leaq	N(%rip), %rsi
	xorl	%eax, %eax
	pushq	%r13
	.cfi_def_cfa_offset 24
	.cfi_offset 13, -24
	pushq	%r12
	.cfi_def_cfa_offset 32
	.cfi_offset 12, -32
	pushq	%rbp
	.cfi_def_cfa_offset 40
	.cfi_offset 6, -40
	pushq	%rbx
	.cfi_def_cfa_offset 48
	.cfi_offset 3, -48
	subq	$16, %rsp
	.cfi_def_cfa_offset 64
	movl	%edi, 12(%rsp)
	leaq	12(%rsp), %rcx
	leaq	.LC3(%rip), %rdi
	call	scanf@PLT
	movl	i(%rip), %edx
	movl	N(%rip), %ebx
	cmpl	%ebx, %edx
	jge	.L3
	movl	M(%rip), %esi
	movl	12(%rsp), %r11d
	xorl	%eax, %eax
	movdqa	.LC4(%rip), %xmm8
	movl	r(%rip), %ecx
	leal	1(%rsi), %ebp
	movd	%esi, %xmm4
	movd	%r11d, %xmm5
	movl	%ebp, %r8d
	movl	%ebp, %r12d
	pshufd	$0, %xmm4, %xmm10
	shrl	$2, %r8d
	andl	$-4, %r12d
	pshufd	$0, %xmm5, %xmm9
	.p2align 4,,10
	.p2align 3
.L9:
	testl	%esi, %esi
	js	.L12
	movl	%ebx, %r9d
	subl	%edx, %r9d
	cmpl	$4, %esi
	jbe	.L13
	movd	%edx, %xmm4
	movd	%r9d, %xmm5
	pxor	%xmm2, %xmm2
	xorl	%eax, %eax
	pshufd	$0, %xmm4, %xmm4
	pshufd	$0, %xmm5, %xmm5
	movdqa	.LC0(%rip), %xmm3
	movdqa	%xmm5, %xmm7
	movdqa	%xmm4, %xmm6
	psrlq	$32, %xmm7
	psrlq	$32, %xmm6
	.p2align 4,,10
	.p2align 3
.L6:
	movdqa	%xmm3, %xmm0
	movdqa	%xmm10, %xmm1
	addl	$1, %eax
	psubd	%xmm0, %xmm1
	paddd	%xmm8, %xmm3
	movdqa	%xmm1, %xmm11
	psrlq	$32, %xmm1
	pmuludq	%xmm5, %xmm11
	pmuludq	%xmm7, %xmm1
	pshufd	$8, %xmm11, %xmm11
	pshufd	$8, %xmm1, %xmm1
	punpckldq	%xmm1, %xmm11
	movdqa	%xmm0, %xmm1
	psrlq	$32, %xmm0
	pmuludq	%xmm4, %xmm1
	pmuludq	%xmm6, %xmm0
	pshufd	$8, %xmm1, %xmm1
	pshufd	$8, %xmm0, %xmm0
	punpckldq	%xmm0, %xmm1
	movdqa	%xmm11, %xmm0
	paddd	%xmm1, %xmm0
	pcmpeqd	%xmm9, %xmm0
	psubd	%xmm0, %xmm2
	cmpl	%r8d, %eax
	jne	.L6
	movdqa	%xmm2, %xmm0
	movl	%r12d, %edi
	psrldq	$8, %xmm0
	paddd	%xmm0, %xmm2
	movdqa	%xmm2, %xmm0
	psrldq	$4, %xmm0
	paddd	%xmm0, %xmm2
	movd	%xmm2, %eax
	addl	%eax, %ecx
	cmpl	%ebp, %r12d
	je	.L8
.L5:
	movl	%esi, %r10d
	movl	%edx, %r13d
	xorl	%eax, %eax
	subl	%edi, %r10d
	imull	%edi, %r13d
	imull	%r9d, %r10d
	addl	%r13d, %r10d
	cmpl	%r11d, %r10d
	sete	%al
	addl	%eax, %ecx
	leal	1(%rdi), %eax
	cmpl	%eax, %esi
	jl	.L8
	movl	%esi, %r10d
	addl	%edx, %r13d
	leal	2(%rdi), %r14d
	subl	%eax, %r10d
	xorl	%eax, %eax
	imull	%r9d, %r10d
	addl	%r13d, %r10d
	cmpl	%r11d, %r10d
	sete	%al
	addl	%eax, %ecx
	cmpl	%r14d, %esi
	jl	.L8
	movl	%esi, %r10d
	addl	%edx, %r13d
	xorl	%eax, %eax
	subl	%r14d, %r10d
	leal	3(%rdi), %r14d
	imull	%r9d, %r10d
	addl	%r13d, %r10d
	cmpl	%r11d, %r10d
	sete	%al
	addl	%eax, %ecx
	cmpl	%r14d, %esi
	jl	.L8
	movl	%esi, %r10d
	leal	(%rdx,%r13), %eax
	subl	%r14d, %r10d
	imull	%r9d, %r10d
	addl	%eax, %r10d
	cmpl	%r11d, %r10d
	sete	%r10b
	addl	$4, %edi
	movzbl	%r10b, %r10d
	addl	%r10d, %ecx
	cmpl	%edi, %esi
	jl	.L8
	movl	%esi, %r10d
	addl	%edx, %eax
	subl	%edi, %r10d
	movl	%r10d, %edi
	imull	%r9d, %edi
	addl	%edi, %eax
	cmpl	%r11d, %eax
	sete	%al
	movzbl	%al, %eax
	addl	%eax, %ecx
.L8:
	movl	%ebp, %edi
	movl	$1, %eax
.L4:
	addl	$1, %edx
	cmpl	%ebx, %edx
	jne	.L9
	movl	%edi, j(%rip)
	movl	%edx, i(%rip)
	testb	%al, %al
	je	.L3
	movl	%ecx, r(%rip)
.L3:
	movl	r(%rip), %eax
	leaq	.LC1(%rip), %rdi
	testl	%eax, %eax
	leaq	.LC2(%rip), %rax
	cmove	%rax, %rdi
	call	puts@PLT
	addq	$16, %rsp
	.cfi_remember_state
	.cfi_def_cfa_offset 48
	xorl	%eax, %eax
	popq	%rbx
	.cfi_def_cfa_offset 40
	popq	%rbp
	.cfi_def_cfa_offset 32
	popq	%r12
	.cfi_def_cfa_offset 24
	popq	%r13
	.cfi_def_cfa_offset 16
	popq	%r14
	.cfi_def_cfa_offset 8
	ret
	.p2align 4,,10
	.p2align 3
.L12:
	.cfi_restore_state
	xorl	%edi, %edi
	jmp	.L4
.L13:
	xorl	%edi, %edi
	jmp	.L5
	.cfi_endproc
.LFE0:
	.size	main, .-main
	.globl	r
	.bss
	.align 4
	.type	r, @object
	.size	r, 4
r:
	.zero	4
	.globl	j
	.align 4
	.type	j, @object
	.size	j, 4
j:
	.zero	4
	.globl	i
	.align 4
	.type	i, @object
	.size	i, 4
i:
	.zero	4
	.globl	M
	.align 4
	.type	M, @object
	.size	M, 4
M:
	.zero	4
	.globl	N
	.align 4
	.type	N, @object
	.size	N, 4
N:
	.zero	4
	.section	.rodata.cst16,"aM",@progbits,16
	.align 16
.LC0:
	.long	0
	.long	1
	.long	2
	.long	3
	.align 16
.LC4:
	.long	4
	.long	4
	.long	4
	.long	4
	.ident	"GCC: (Ubuntu 11.4.0-1ubuntu1~22.04) 11.4.0"
	.section	.note.GNU-stack,"",@progbits
	.section	.note.gnu.property,"a"
	.align 8
	.long	1f - 0f
	.long	4f - 1f
	.long	5
0:
	.string	"GNU"
1:
	.align 8
	.long	0xc0000002
	.long	3f - 2f
2:
	.long	0x3
3:
	.align 8
4:
```
```c
N;M;i;j;r;main(K){for(scanf("%d%d%d",&N,&M,&K);i<N;++i)for(j=0;j<=M;++j)r+=i*j+(N-i)*(M-j)==K;puts(r?"Yes":"No");}```
Given the following C code, your task is to generate highly optimized x86-64 assembly code.
C Code:

```c
N;M;i;j;r;main(K){for(scanf("%d%d%d",&N,&M,&K);i<N;++i)for(j=0;j<=M;++j)r+=i*j+(N-i)*(M-j)==K;puts(r?"Yes":"No");}```

Only output the optimized assembly code. Do not include any other text. Do not write any comments in the assembly code. Wrap the assembly code in ```assembly``` tags.
Optimized Assembly Code:

4 2 2
 4 2 1
 7 9 8
 2 5 8
 6 2 2
 7 17 8
 1 5 8
 2 3 2
 7 17 5
 2 1 8

Yes
 No
 No
 Yes
 Yes
 No
 No
 Yes
 No
 No

Given the following C code and assembly code, your task is to generate highly optimized x86-64 assembly code.
C Code:

```c
N;M;i;j;r;main(K){for(scanf("%d%d%d",&N,&M,&K);i<N;++i)for(j=0;j<=M;++j)r+=i*j+(N-i)*(M-j)==K;puts(r?"Yes":"No");}```

Assembly Code:

```assembly
	.file	"temp.c"
	.text
	.section	.rodata.str1.1,"aMS",@progbits,1
.LC1:
	.string	"Yes"
.LC2:
	.string	"No"
.LC3:
	.string	"%d%d%d"
	.section	.text.startup,"ax",@progbits
	.p2align 4
	.globl	main
	.type	main, @function
main:
.LFB0:
	.cfi_startproc
	endbr64
	pushq	%r14
	.cfi_def_cfa_offset 16
	.cfi_offset 14, -16
	leaq	M(%rip), %rdx
	leaq	N(%rip), %rsi
	xorl	%eax, %eax
	pushq	%r13
	.cfi_def_cfa_offset 24
	.cfi_offset 13, -24
	pushq	%r12
	.cfi_def_cfa_offset 32
	.cfi_offset 12, -32
	pushq	%rbp
	.cfi_def_cfa_offset 40
	.cfi_offset 6, -40
	pushq	%rbx
	.cfi_def_cfa_offset 48
	.cfi_offset 3, -48
	subq	$16, %rsp
	.cfi_def_cfa_offset 64
	movl	%edi, 12(%rsp)
	leaq	12(%rsp), %rcx
	leaq	.LC3(%rip), %rdi
	call	scanf@PLT
	movl	i(%rip), %edx
	movl	N(%rip), %ebx
	cmpl	%ebx, %edx
	jge	.L3
	movl	M(%rip), %esi
	movl	12(%rsp), %r11d
	xorl	%eax, %eax
	movdqa	.LC4(%rip), %xmm8
	movl	r(%rip), %ecx
	leal	1(%rsi), %ebp
	movd	%esi, %xmm4
	movd	%r11d, %xmm5
	movl	%ebp, %r8d
	movl	%ebp, %r12d
	pshufd	$0, %xmm4, %xmm10
	shrl	$2, %r8d
	andl	$-4, %r12d
	pshufd	$0, %xmm5, %xmm9
	.p2align 4,,10
	.p2align 3
.L9:
	testl	%esi, %esi
	js	.L12
	movl	%ebx, %r9d
	subl	%edx, %r9d
	cmpl	$4, %esi
	jbe	.L13
	movd	%edx, %xmm4
	movd	%r9d, %xmm5
	pxor	%xmm2, %xmm2
	xorl	%eax, %eax
	pshufd	$0, %xmm4, %xmm4
	pshufd	$0, %xmm5, %xmm5
	movdqa	.LC0(%rip), %xmm3
	movdqa	%xmm5, %xmm7
	movdqa	%xmm4, %xmm6
	psrlq	$32, %xmm7
	psrlq	$32, %xmm6
	.p2align 4,,10
	.p2align 3
.L6:
	movdqa	%xmm3, %xmm0
	movdqa	%xmm10, %xmm1
	addl	$1, %eax
	psubd	%xmm0, %xmm1
	paddd	%xmm8, %xmm3
	movdqa	%xmm1, %xmm11
	psrlq	$32, %xmm1
	pmuludq	%xmm5, %xmm11
	pmuludq	%xmm7, %xmm1
	pshufd	$8, %xmm11, %xmm11
	pshufd	$8, %xmm1, %xmm1
	punpckldq	%xmm1, %xmm11
	movdqa	%xmm0, %xmm1
	psrlq	$32, %xmm0
	pmuludq	%xmm4, %xmm1
	pmuludq	%xmm6, %xmm0
	pshufd	$8, %xmm1, %xmm1
	pshufd	$8, %xmm0, %xmm0
	punpckldq	%xmm0, %xmm1
	movdqa	%xmm11, %xmm0
	paddd	%xmm1, %xmm0
	pcmpeqd	%xmm9, %xmm0
	psubd	%xmm0, %xmm2
	cmpl	%r8d, %eax
	jne	.L6
	movdqa	%xmm2, %xmm0
	movl	%r12d, %edi
	psrldq	$8, %xmm0
	paddd	%xmm0, %xmm2
	movdqa	%xmm2, %xmm0
	psrldq	$4, %xmm0
	paddd	%xmm0, %xmm2
	movd	%xmm2, %eax
	addl	%eax, %ecx
	cmpl	%ebp, %r12d
	je	.L8
.L5:
	movl	%esi, %r10d
	movl	%edx, %r13d
	xorl	%eax, %eax
	subl	%edi, %r10d
	imull	%edi, %r13d
	imull	%r9d, %r10d
	addl	%r13d, %r10d
	cmpl	%r11d, %r10d
	sete	%al
	addl	%eax, %ecx
	leal	1(%rdi), %eax
	cmpl	%eax, %esi
	jl	.L8
	movl	%esi, %r10d
	addl	%edx, %r13d
	leal	2(%rdi), %r14d
	subl	%eax, %r10d
	xorl	%eax, %eax
	imull	%r9d, %r10d
	addl	%r13d, %r10d
	cmpl	%r11d, %r10d
	sete	%al
	addl	%eax, %ecx
	cmpl	%r14d, %esi
	jl	.L8
	movl	%esi, %r10d
	addl	%edx, %r13d
	xorl	%eax, %eax
	subl	%r14d, %r10d
	leal	3(%rdi), %r14d
	imull	%r9d, %r10d
	addl	%r13d, %r10d
	cmpl	%r11d, %r10d
	sete	%al
	addl	%eax, %ecx
	cmpl	%r14d, %esi
	jl	.L8
	movl	%esi, %r10d
	leal	(%rdx,%r13), %eax
	subl	%r14d, %r10d
	imull	%r9d, %r10d
	addl	%eax, %r10d
	cmpl	%r11d, %r10d
	sete	%r10b
	addl	$4, %edi
	movzbl	%r10b, %r10d
	addl	%r10d, %ecx
	cmpl	%edi, %esi
	jl	.L8
	movl	%esi, %r10d
	addl	%edx, %eax
	subl	%edi, %r10d
	movl	%r10d, %edi
	imull	%r9d, %edi
	addl	%edi, %eax
	cmpl	%r11d, %eax
	sete	%al
	movzbl	%al, %eax
	addl	%eax, %ecx
.L8:
	movl	%ebp, %edi
	movl	$1, %eax
.L4:
	addl	$1, %edx
	cmpl	%ebx, %edx
	jne	.L9
	movl	%edi, j(%rip)
	movl	%edx, i(%rip)
	testb	%al, %al
	je	.L3
	movl	%ecx, r(%rip)
.L3:
	movl	r(%rip), %eax
	leaq	.LC1(%rip), %rdi
	testl	%eax, %eax
	leaq	.LC2(%rip), %rax
	cmove	%rax, %rdi
	call	puts@PLT
	addq	$16, %rsp
	.cfi_remember_state
	.cfi_def_cfa_offset 48
	xorl	%eax, %eax
	popq	%rbx
	.cfi_def_cfa_offset 40
	popq	%rbp
	.cfi_def_cfa_offset 32
	popq	%r12
	.cfi_def_cfa_offset 24
	popq	%r13
	.cfi_def_cfa_offset 16
	popq	%r14
	.cfi_def_cfa_offset 8
	ret
	.p2align 4,,10
	.p2align 3
.L12:
	.cfi_restore_state
	xorl	%edi, %edi
	jmp	.L4
.L13:
	xorl	%edi, %edi
	jmp	.L5
	.cfi_endproc
.LFE0:
	.size	main, .-main
	.globl	r
	.bss
	.align 4
	.type	r, @object
	.size	r, 4
r:
	.zero	4
	.globl	j
	.align 4
	.type	j, @object
	.size	j, 4
j:
	.zero	4
	.globl	i
	.align 4
	.type	i, @object
	.size	i, 4
i:
	.zero	4
	.globl	M
	.align 4
	.type	M, @object
	.size	M, 4
M:
	.zero	4
	.globl	N
	.align 4
	.type	N, @object
	.size	N, 4
N:
	.zero	4
	.section	.rodata.cst16,"aM",@progbits,16
	.align 16
.LC0:
	.long	0
	.long	1
	.long	2
	.long	3
	.align 16
.LC4:
	.long	4
	.long	4
	.long	4
	.long	4
	.ident	"GCC: (Ubuntu 11.4.0-1ubuntu1~22.04) 11.4.0"
	.section	.note.GNU-stack,"",@progbits
	.section	.note.gnu.property,"a"
	.align 8
	.long	1f - 0f
	.long	4f - 1f
	.long	5
0:
	.string	"GNU"
1:
	.align 8
	.long	0xc0000002
	.long	3f - 2f
2:
	.long	0x3
3:
	.align 8
4:
```

Only output the optimized assembly code. Do not include any other text. Do not write any comments in the assembly code. Wrap the assembly code in ```assembly``` tags.
Optimized Assembly Code:

train
```assembly
	.file	"temp.c"
	.text
	.section	.rodata.str1.1,"aMS",@progbits,1
.LC1:
	.string	"Yes"
.LC2:
	.string	"No"
.LC3:
	.string	"%d%d%d"
	.section	.text.startup,"ax",@progbits
	.p2align 4
	.globl	main
	.type	main, @function
main:
.LFB0:
	.cfi_startproc
	endbr64
	pushq	%r14
	.cfi_def_cfa_offset 16
	.cfi_offset 14, -16
	leaq	M(%rip), %rdx
	leaq	N(%rip), %rsi
	xorl	%eax, %eax
	pushq	%r13
	.cfi_def_cfa_offset 24
	.cfi_offset 13, -24
	pushq	%r12
	.cfi_def_cfa_offset 32
	.cfi_offset 12, -32
	pushq	%rbp
	.cfi_def_cfa_offset 40
	.cfi_offset 6, -40
	pushq	%rbx
	.cfi_def_cfa_offset 48
	.cfi_offset 3, -48
	subq	$16, %rsp
	.cfi_def_cfa_offset 64
	movl	%edi, 12(%rsp)
	leaq	12(%rsp), %rcx
	leaq	.LC3(%rip), %rdi
	call	scanf@PLT
	movl	i(%rip), %edx
	movl	N(%rip), %ebx
	cmpl	%ebx, %edx
	jge	.L3
	movl	M(%rip), %esi
	movl	12(%rsp), %r11d
	xorl	%eax, %eax
	movdqa	.LC4(%rip), %xmm8
	movl	r(%rip), %ecx
	leal	1(%rsi), %ebp
	movd	%esi, %xmm4
	movd	%r11d, %xmm5
	movl	%ebp, %r8d
	movl	%ebp, %r12d
	pshufd	$0, %xmm4, %xmm10
	shrl	$2, %r8d
	andl	$-4, %r12d
	pshufd	$0, %xmm5, %xmm9
	.p2align 4,,10
	.p2align 3
.L9:
	testl	%esi, %esi
	js	.L12
	movl	%ebx, %r9d
	subl	%edx, %r9d
	cmpl	$4, %esi
	jbe	.L13
	movd	%edx, %xmm4
	movd	%r9d, %xmm5
	pxor	%xmm2, %xmm2
	xorl	%eax, %eax
	pshufd	$0, %xmm4, %xmm4
	pshufd	$0, %xmm5, %xmm5
	movdqa	.LC0(%rip), %xmm3
	movdqa	%xmm5, %xmm7
	movdqa	%xmm4, %xmm6
	psrlq	$32, %xmm7
	psrlq	$32, %xmm6
	.p2align 4,,10
	.p2align 3
.L6:
	movdqa	%xmm3, %xmm0
	movdqa	%xmm10, %xmm1
	addl	$1, %eax
	psubd	%xmm0, %xmm1
	paddd	%xmm8, %xmm3
	movdqa	%xmm1, %xmm11
	psrlq	$32, %xmm1
	pmuludq	%xmm5, %xmm11
	pmuludq	%xmm7, %xmm1
	pshufd	$8, %xmm11, %xmm11
	pshufd	$8, %xmm1, %xmm1
	punpckldq	%xmm1, %xmm11
	movdqa	%xmm0, %xmm1
	psrlq	$32, %xmm0
	pmuludq	%xmm4, %xmm1
	pmuludq	%xmm6, %xmm0
	pshufd	$8, %xmm1, %xmm1
	pshufd	$8, %xmm0, %xmm0
	punpckldq	%xmm0, %xmm1
	movdqa	%xmm11, %xmm0
	paddd	%xmm1, %xmm0
	pcmpeqd	%xmm9, %xmm0
	psubd	%xmm0, %xmm2
	cmpl	%r8d, %eax
	jne	.L6
	movdqa	%xmm2, %xmm0
	movl	%r12d, %edi
	psrldq	$8, %xmm0
	paddd	%xmm0, %xmm2
	movdqa	%xmm2, %xmm0
	psrldq	$4, %xmm0
	paddd	%xmm0, %xmm2
	movd	%xmm2, %eax
	addl	%eax, %ecx
	cmpl	%ebp, %r12d
	je	.L8
.L5:
	movl	%esi, %r10d
	movl	%edx, %r13d
	xorl	%eax, %eax
	subl	%edi, %r10d
	imull	%edi, %r13d
	imull	%r9d, %r10d
	addl	%r13d, %r10d
	cmpl	%r11d, %r10d
	sete	%al
	addl	%eax, %ecx
	leal	1(%rdi), %eax
	cmpl	%eax, %esi
	jl	.L8
	movl	%esi, %r10d
	addl	%edx, %r13d
	leal	2(%rdi), %r14d
	subl	%eax, %r10d
	xorl	%eax, %eax
	imull	%r9d, %r10d
	addl	%r13d, %r10d
	cmpl	%r11d, %r10d
	sete	%al
	addl	%eax, %ecx
	cmpl	%r14d, %esi
	jl	.L8
	movl	%esi, %r10d
	addl	%edx, %r13d
	xorl	%eax, %eax
	subl	%r14d, %r10d
	leal	3(%rdi), %r14d
	imull	%r9d, %r10d
	addl	%r13d, %r10d
	cmpl	%r11d, %r10d
	sete	%al
	addl	%eax, %ecx
	cmpl	%r14d, %esi
	jl	.L8
	movl	%esi, %r10d
	leal	(%rdx,%r13), %eax
	subl	%r14d, %r10d
	imull	%r9d, %r10d
	addl	%eax, %r10d
	cmpl	%r11d, %r10d
	sete	%r10b
	addl	$4, %edi
	movzbl	%r10b, %r10d
	addl	%r10d, %ecx
	cmpl	%edi, %esi
	jl	.L8
	movl	%esi, %r10d
	addl	%edx, %eax
	subl	%edi, %r10d
	movl	%r10d, %edi
	imull	%r9d, %edi
	addl	%edi, %eax
	cmpl	%r11d, %eax
	sete	%al
	movzbl	%al, %eax
	addl	%eax, %ecx
.L8:
	movl	%ebp, %edi
	movl	$1, %eax
.L4:
	addl	$1, %edx
	cmpl	%ebx, %edx
	jne	.L9
	movl	%edi, j(%rip)
	movl	%edx, i(%rip)
	testb	%al, %al
	je	.L3
	movl	%ecx, r(%rip)
.L3:
	movl	r(%rip), %eax
	leaq	.LC1(%rip), %rdi
	testl	%eax, %eax
	leaq	.LC2(%rip), %rax
	cmove	%rax, %rdi
	call	puts@PLT
	addq	$16, %rsp
	.cfi_remember_state
	.cfi_def_cfa_offset 48
	xorl	%eax, %eax
	popq	%rbx
	.cfi_def_cfa_offset 40
	popq	%rbp
	.cfi_def_cfa_offset 32
	popq	%r12
	.cfi_def_cfa_offset 24
	popq	%r13
	.cfi_def_cfa_offset 16
	popq	%r14
	.cfi_def_cfa_offset 8
	ret
	.p2align 4,,10
	.p2align 3
.L12:
	.cfi_restore_state
	xorl	%edi, %edi
	jmp	.L4
.L13:
	xorl	%edi, %edi
	jmp	.L5
	.cfi_endproc
.LFE0:
	.size	main, .-main
	.globl	r
	.bss
	.align 4
	.type	r, @object
	.size	r, 4
r:
	.zero	4
	.globl	j
	.align 4
	.type	j, @object
	.size	j, 4
j:
	.zero	4
	.globl	i
	.align 4
	.type	i, @object
	.size	i, 4
i:
	.zero	4
	.globl	M
	.align 4
	.type	M, @object
	.size	M, 4
M:
	.zero	4
	.globl	N
	.align 4
	.type	N, @object
	.size	N, 4
N:
	.zero	4
	.section	.rodata.cst16,"aM",@progbits,16
	.align 16
.LC0:
	.long	0
	.long	1
	.long	2
	.long	3
	.align 16
.LC4:
	.long	4
	.long	4
	.long	4
	.long	4
	.ident	"GCC: (Ubuntu 11.4.0-1ubuntu1~22.04) 11.4.0"
	.section	.note.GNU-stack,"",@progbits
	.section	.note.gnu.property,"a"
	.align 8
	.long	1f - 0f
	.long	4f - 1f
	.long	5
0:
	.string	"GNU"
1:
	.align 8
	.long	0xc0000002
	.long	3f - 2f
2:
	.long	0x3
3:
	.align 8
4:
```