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

```c
#include<stdio.h>

int main(void)
{
  int a,b,k;
  scanf("%d%d%d",&a,&b,&k);

  int i,c[100],j=0;
  for(i=1;(i<=a)||(i<=b);i++)
    if((a%i==0)&&(b%i==0)){
      j++;
      c[j]=i;
    }

  printf("%d\n",c[j-k+1]);
  return 0;
}```

Unoptimized Assembly Code:

```assembly
	.file	"temp.c"
	.text
	.section	.rodata
.LC0:
	.string	"%d%d%d"
.LC1:
	.string	"%d\n"
	.text
	.globl	main
	.type	main, @function
main:
.LFB0:
	.cfi_startproc
	endbr64
	pushq	%rbp
	.cfi_def_cfa_offset 16
	.cfi_offset 6, -16
	movq	%rsp, %rbp
	.cfi_def_cfa_register 6
	subq	$448, %rsp
	movq	%fs:40, %rax
	movq	%rax, -8(%rbp)
	xorl	%eax, %eax
	leaq	-428(%rbp), %rcx
	leaq	-432(%rbp), %rdx
	leaq	-436(%rbp), %rax
	movq	%rax, %rsi
	leaq	.LC0(%rip), %rax
	movq	%rax, %rdi
	movl	$0, %eax
	call	__isoc99_scanf@PLT
	movl	$0, -420(%rbp)
	movl	$1, -424(%rbp)
	jmp	.L2
.L4:
	movl	-436(%rbp), %eax
	cltd
	idivl	-424(%rbp)
	movl	%edx, %eax
	testl	%eax, %eax
	jne	.L3
	movl	-432(%rbp), %eax
	cltd
	idivl	-424(%rbp)
	movl	%edx, %eax
	testl	%eax, %eax
	jne	.L3
	addl	$1, -420(%rbp)
	movl	-420(%rbp), %eax
	cltq
	movl	-424(%rbp), %edx
	movl	%edx, -416(%rbp,%rax,4)
.L3:
	addl	$1, -424(%rbp)
.L2:
	movl	-436(%rbp), %eax
	cmpl	%eax, -424(%rbp)
	jle	.L4
	movl	-432(%rbp), %eax
	cmpl	%eax, -424(%rbp)
	jle	.L4
	movl	-428(%rbp), %edx
	movl	-420(%rbp), %eax
	subl	%edx, %eax
	addl	$1, %eax
	cltq
	movl	-416(%rbp,%rax,4), %eax
	movl	%eax, %esi
	leaq	.LC1(%rip), %rax
	movq	%rax, %rdi
	movl	$0, %eax
	call	printf@PLT
	movl	$0, %eax
	movq	-8(%rbp), %rdx
	subq	%fs:40, %rdx
	je	.L6
	call	__stack_chk_fail@PLT
.L6:
	leave
	.cfi_def_cfa 7, 8
	ret
	.cfi_endproc
.LFE0:
	.size	main, .-main
	.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.
user
	.file	"temp.c"
	.text
	.section	.rodata.str1.1,"aMS",@progbits,1
.LC0:
	.string	"%d%d%d"
.LC1:
	.string	"%d\n"
	.section	.text.startup,"ax",@progbits
	.p2align 4
	.globl	main
	.type	main, @function
main:
.LFB23:
	.cfi_startproc
	endbr64
	subq	$440, %rsp
	.cfi_def_cfa_offset 448
	leaq	.LC0(%rip), %rdi
	movq	%fs:40, %rax
	movq	%rax, 424(%rsp)
	xorl	%eax, %eax
	leaq	12(%rsp), %rcx
	leaq	4(%rsp), %rsi
	leaq	8(%rsp), %rdx
	call	__isoc99_scanf@PLT
	movl	4(%rsp), %esi
	movl	8(%rsp), %edi
	xorl	%r8d, %r8d
	movl	$1, %ecx
	jmp	.L2
	.p2align 4,,10
	.p2align 3
.L4:
	movl	%esi, %eax
	cltd
	idivl	%ecx
	testl	%edx, %edx
	jne	.L3
	movl	%edi, %eax
	cltd
	idivl	%ecx
	testl	%edx, %edx
	jne	.L3
	addl	$1, %r8d
	movslq	%r8d, %rax
	movl	%ecx, 16(%rsp,%rax,4)
.L3:
	addl	$1, %ecx
.L2:
	cmpl	%ecx, %esi
	jge	.L4
	cmpl	%ecx, %edi
	jge	.L4
	subl	12(%rsp), %r8d
	leaq	.LC1(%rip), %rsi
	movl	$1, %edi
	leal	1(%r8), %eax
	cltq
	movl	16(%rsp,%rax,4), %edx
	xorl	%eax, %eax
	call	__printf_chk@PLT
	movq	424(%rsp), %rax
	subq	%fs:40, %rax
	jne	.L8
	xorl	%eax, %eax
	addq	$440, %rsp
	.cfi_remember_state
	.cfi_def_cfa_offset 8
	ret
.L8:
	.cfi_restore_state
	call	__stack_chk_fail@PLT
	.cfi_endproc
.LFE23:
	.size	main, .-main
	.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
	.file	"temp.c"
	.text
	.section	.rodata.str1.1,"aMS",@progbits,1
.LC0:
	.string	"%d%d%d"
.LC1:
	.string	"%d\n"
	.section	.text.startup,"ax",@progbits
	.p2align 4
	.globl	main
	.type	main, @function
main:
.LFB23:
	.cfi_startproc
	endbr64
	subq	$440, %rsp
	.cfi_def_cfa_offset 448
	leaq	.LC0(%rip), %rdi
	movq	%fs:40, %rax
	movq	%rax, 424(%rsp)
	xorl	%eax, %eax
	leaq	12(%rsp), %rcx
	leaq	4(%rsp), %rsi
	leaq	8(%rsp), %rdx
	call	__isoc99_scanf@PLT
	movl	4(%rsp), %esi
	movl	8(%rsp), %edi
	xorl	%r8d, %r8d
	movl	$1, %ecx
	jmp	.L2
	.p2align 4,,10
	.p2align 3
.L4:
	movl	%esi, %eax
	cltd
	idivl	%ecx
	testl	%edx, %edx
	jne	.L3
	movl	%edi, %eax
	cltd
	idivl	%ecx
	testl	%edx, %edx
	jne	.L3
	addl	$1, %r8d
	movslq	%r8d, %rax
	movl	%ecx, 16(%rsp,%rax,4)
.L3:
	addl	$1, %ecx
.L2:
	cmpl	%ecx, %esi
	jge	.L4
	cmpl	%ecx, %edi
	jge	.L4
	subl	12(%rsp), %r8d
	leaq	.LC1(%rip), %rsi
	movl	$1, %edi
	leal	1(%r8), %eax
	cltq
	movl	16(%rsp,%rax,4), %edx
	xorl	%eax, %eax
	call	__printf_chk@PLT
	movq	424(%rsp), %rax
	subq	%fs:40, %rax
	jne	.L8
	xorl	%eax, %eax
	addq	$440, %rsp
	.cfi_remember_state
	.cfi_def_cfa_offset 8
	ret
.L8:
	.cfi_restore_state
	call	__stack_chk_fail@PLT
	.cfi_endproc
.LFE23:
	.size	main, .-main
	.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:

#include<stdio.h>

int main(void)
{
  int a,b,k;
  scanf("%d%d%d",&a,&b,&k);

  int i,c[100],j=0;
  for(i=1;(i<=a)||(i<=b);i++)
    if((a%i==0)&&(b%i==0)){
      j++;
      c[j]=i;
    }

  printf("%d\n",c[j-k+1]);
  return 0;
}
100 50 2
 16 12 2
 12 12 2
 100 45 2
 27 12 1
 16 24 1
 110 50 2
 12 12 3
 27 18 1
 100 50 3

25
 2
 6
 1
 3
 8
 5
 4
 9
 10

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

```c
#include<stdio.h>

int main(void)
{
  int a,b,k;
  scanf("%d%d%d",&a,&b,&k);

  int i,c[100],j=0;
  for(i=1;(i<=a)||(i<=b);i++)
    if((a%i==0)&&(b%i==0)){
      j++;
      c[j]=i;
    }

  printf("%d\n",c[j-k+1]);
  return 0;
}```

Unoptimized Assembly Code:

```assembly
	.file	"temp.c"
	.text
	.section	.rodata
.LC0:
	.string	"%d%d%d"
.LC1:
	.string	"%d\n"
	.text
	.globl	main
	.type	main, @function
main:
.LFB0:
	.cfi_startproc
	endbr64
	pushq	%rbp
	.cfi_def_cfa_offset 16
	.cfi_offset 6, -16
	movq	%rsp, %rbp
	.cfi_def_cfa_register 6
	subq	$448, %rsp
	movq	%fs:40, %rax
	movq	%rax, -8(%rbp)
	xorl	%eax, %eax
	leaq	-428(%rbp), %rcx
	leaq	-432(%rbp), %rdx
	leaq	-436(%rbp), %rax
	movq	%rax, %rsi
	leaq	.LC0(%rip), %rax
	movq	%rax, %rdi
	movl	$0, %eax
	call	__isoc99_scanf@PLT
	movl	$0, -420(%rbp)
	movl	$1, -424(%rbp)
	jmp	.L2
.L4:
	movl	-436(%rbp), %eax
	cltd
	idivl	-424(%rbp)
	movl	%edx, %eax
	testl	%eax, %eax
	jne	.L3
	movl	-432(%rbp), %eax
	cltd
	idivl	-424(%rbp)
	movl	%edx, %eax
	testl	%eax, %eax
	jne	.L3
	addl	$1, -420(%rbp)
	movl	-420(%rbp), %eax
	cltq
	movl	-424(%rbp), %edx
	movl	%edx, -416(%rbp,%rax,4)
.L3:
	addl	$1, -424(%rbp)
.L2:
	movl	-436(%rbp), %eax
	cmpl	%eax, -424(%rbp)
	jle	.L4
	movl	-432(%rbp), %eax
	cmpl	%eax, -424(%rbp)
	jle	.L4
	movl	-428(%rbp), %edx
	movl	-420(%rbp), %eax
	subl	%edx, %eax
	addl	$1, %eax
	cltq
	movl	-416(%rbp,%rax,4), %eax
	movl	%eax, %esi
	leaq	.LC1(%rip), %rax
	movq	%rax, %rdi
	movl	$0, %eax
	call	printf@PLT
	movl	$0, %eax
	movq	-8(%rbp), %rdx
	subq	%fs:40, %rdx
	je	.L6
	call	__stack_chk_fail@PLT
.L6:
	leave
	.cfi_def_cfa 7, 8
	ret
	.cfi_endproc
.LFE0:
	.size	main, .-main
	.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.
val
	.file	"temp.c"
	.text
	.section	.rodata
.LC0:
	.string	"%d%d%d"
.LC1:
	.string	"%d\n"
	.text
	.globl	main
	.type	main, @function
main:
.LFB0:
	.cfi_startproc
	endbr64
	pushq	%rbp
	.cfi_def_cfa_offset 16
	.cfi_offset 6, -16
	movq	%rsp, %rbp
	.cfi_def_cfa_register 6
	subq	$448, %rsp
	movq	%fs:40, %rax
	movq	%rax, -8(%rbp)
	xorl	%eax, %eax
	leaq	-428(%rbp), %rcx
	leaq	-432(%rbp), %rdx
	leaq	-436(%rbp), %rax
	movq	%rax, %rsi
	leaq	.LC0(%rip), %rax
	movq	%rax, %rdi
	movl	$0, %eax
	call	__isoc99_scanf@PLT
	movl	$0, -420(%rbp)
	movl	$1, -424(%rbp)
	jmp	.L2
.L4:
	movl	-436(%rbp), %eax
	cltd
	idivl	-424(%rbp)
	movl	%edx, %eax
	testl	%eax, %eax
	jne	.L3
	movl	-432(%rbp), %eax
	cltd
	idivl	-424(%rbp)
	movl	%edx, %eax
	testl	%eax, %eax
	jne	.L3
	addl	$1, -420(%rbp)
	movl	-420(%rbp), %eax
	cltq
	movl	-424(%rbp), %edx
	movl	%edx, -416(%rbp,%rax,4)
.L3:
	addl	$1, -424(%rbp)
.L2:
	movl	-436(%rbp), %eax
	cmpl	%eax, -424(%rbp)
	jle	.L4
	movl	-432(%rbp), %eax
	cmpl	%eax, -424(%rbp)
	jle	.L4
	movl	-428(%rbp), %edx
	movl	-420(%rbp), %eax
	subl	%edx, %eax
	addl	$1, %eax
	cltq
	movl	-416(%rbp,%rax,4), %eax
	movl	%eax, %esi
	leaq	.LC1(%rip), %rax
	movq	%rax, %rdi
	movl	$0, %eax
	call	printf@PLT
	movl	$0, %eax
	movq	-8(%rbp), %rdx
	subq	%fs:40, %rdx
	je	.L6
	call	__stack_chk_fail@PLT
.L6:
	leave
	.cfi_def_cfa 7, 8
	ret
	.cfi_endproc
.LFE0:
	.size	main, .-main
	.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:
