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>
#include<stdlib.h>
#include<string.h>

int main(void) {
	int i;
	int K, S;
	int remaining;
	int x, y, z;
	int patterns;
	char buf[128], *ch;

	fgets(buf, sizeof(buf), stdin);
	ch = strtok(buf, " ");
	K = atoi(ch);
	ch = strtok(NULL, " ");
	S = atoi(ch);

	patterns = 0;
	for(x = 0; x <= K; x += 1) {
		remaining = S - x;
		if(remaining < 0) {
			break;
		}
		for(y = 0; y <= K; y += 1) {
			remaining = S - x - y;
			if(remaining < 0) {
				break;
			}
			if(remaining <= K) {
				patterns += 1;
			}
		}
	}

	printf("%d\n", patterns);

	return 0;
}
```

Unoptimized Assembly Code:

```assembly
	.file	"temp.c"
	.text
	.section	.rodata
.LC0:
	.string	" "
.LC1:
	.string	"%d\n"
	.text
	.globl	main
	.type	main, @function
main:
.LFB6:
	.cfi_startproc
	endbr64
	pushq	%rbp
	.cfi_def_cfa_offset 16
	.cfi_offset 6, -16
	movq	%rsp, %rbp
	.cfi_def_cfa_register 6
	subq	$176, %rsp
	movq	%fs:40, %rax
	movq	%rax, -8(%rbp)
	xorl	%eax, %eax
	movq	stdin(%rip), %rdx
	leaq	-144(%rbp), %rax
	movl	$128, %esi
	movq	%rax, %rdi
	call	fgets@PLT
	leaq	-144(%rbp), %rax
	leaq	.LC0(%rip), %rdx
	movq	%rdx, %rsi
	movq	%rax, %rdi
	call	strtok@PLT
	movq	%rax, -152(%rbp)
	movq	-152(%rbp), %rax
	movq	%rax, %rdi
	call	atoi@PLT
	movl	%eax, -164(%rbp)
	leaq	.LC0(%rip), %rax
	movq	%rax, %rsi
	movl	$0, %edi
	call	strtok@PLT
	movq	%rax, -152(%rbp)
	movq	-152(%rbp), %rax
	movq	%rax, %rdi
	call	atoi@PLT
	movl	%eax, -160(%rbp)
	movl	$0, -168(%rbp)
	movl	$0, -176(%rbp)
	jmp	.L2
.L10:
	movl	-160(%rbp), %eax
	subl	-176(%rbp), %eax
	movl	%eax, -156(%rbp)
	cmpl	$0, -156(%rbp)
	js	.L13
	movl	$0, -172(%rbp)
	jmp	.L5
.L9:
	movl	-160(%rbp), %eax
	subl	-176(%rbp), %eax
	subl	-172(%rbp), %eax
	movl	%eax, -156(%rbp)
	cmpl	$0, -156(%rbp)
	js	.L14
	movl	-156(%rbp), %eax
	cmpl	-164(%rbp), %eax
	jg	.L8
	addl	$1, -168(%rbp)
.L8:
	addl	$1, -172(%rbp)
.L5:
	movl	-172(%rbp), %eax
	cmpl	-164(%rbp), %eax
	jle	.L9
	jmp	.L7
.L14:
	nop
.L7:
	addl	$1, -176(%rbp)
.L2:
	movl	-176(%rbp), %eax
	cmpl	-164(%rbp), %eax
	jle	.L10
	jmp	.L4
.L13:
	nop
.L4:
	movl	-168(%rbp), %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	.L12
	call	__stack_chk_fail@PLT
.L12:
	leave
	.cfi_def_cfa 7, 8
	ret
	.cfi_endproc
.LFE6:
	.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	" "
.LC1:
	.string	"%d\n"
	.section	.text.startup,"ax",@progbits
	.p2align 4
	.globl	main
	.type	main, @function
main:
.LFB51:
	.cfi_startproc
	endbr64
	pushq	%r12
	.cfi_def_cfa_offset 16
	.cfi_offset 12, -16
	movl	$128, %esi
	leaq	.LC0(%rip), %r12
	pushq	%rbp
	.cfi_def_cfa_offset 24
	.cfi_offset 6, -24
	pushq	%rbx
	.cfi_def_cfa_offset 32
	.cfi_offset 3, -32
	subq	$144, %rsp
	.cfi_def_cfa_offset 176
	movq	stdin(%rip), %rdx
	movq	%fs:40, %rax
	movq	%rax, 136(%rsp)
	xorl	%eax, %eax
	movq	%rsp, %rbp
	movq	%rbp, %rdi
	call	fgets@PLT
	movq	%rbp, %rdi
	movq	%r12, %rsi
	call	strtok@PLT
	movl	$10, %edx
	xorl	%esi, %esi
	movq	%rax, %rdi
	call	strtol@PLT
	xorl	%edi, %edi
	movq	%r12, %rsi
	movq	%rax, %rbp
	movl	%eax, %ebx
	call	strtok@PLT
	xorl	%esi, %esi
	movl	$10, %edx
	movq	%rax, %rdi
	call	strtol@PLT
	orl	%eax, %ebp
	js	.L10
	movl	%eax, %edi
	xorl	%edx, %edx
	leal	1(%rax), %r8d
	.p2align 4,,10
	.p2align 3
.L3:
	testl	%edi, %edi
	js	.L4
	movl	%edi, %eax
	leal	1(%rdi), %esi
	jmp	.L5
	.p2align 4,,10
	.p2align 3
.L7:
	subl	$1, %eax
	jb	.L4
.L5:
	xorl	%ecx, %ecx
	cmpl	%eax, %ebx
	setge	%cl
	addl	%ecx, %edx
	movl	%esi, %ecx
	subl	%eax, %ecx
	cmpl	%ebx, %ecx
	jle	.L7
.L4:
	movl	%r8d, %eax
	subl	%edi, %eax
	cmpl	%eax, %ebx
	jl	.L2
	subl	$1, %edi
	jnb	.L3
.L2:
	xorl	%eax, %eax
	leaq	.LC1(%rip), %rsi
	movl	$1, %edi
	call	__printf_chk@PLT
	movq	136(%rsp), %rax
	subq	%fs:40, %rax
	jne	.L19
	addq	$144, %rsp
	.cfi_remember_state
	.cfi_def_cfa_offset 32
	xorl	%eax, %eax
	popq	%rbx
	.cfi_def_cfa_offset 24
	popq	%rbp
	.cfi_def_cfa_offset 16
	popq	%r12
	.cfi_def_cfa_offset 8
	ret
.L10:
	.cfi_restore_state
	xorl	%edx, %edx
	jmp	.L2
.L19:
	call	__stack_chk_fail@PLT
	.cfi_endproc
.LFE51:
	.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	" "
.LC1:
	.string	"%d\n"
	.section	.text.startup,"ax",@progbits
	.p2align 4
	.globl	main
	.type	main, @function
main:
.LFB51:
	.cfi_startproc
	endbr64
	pushq	%r12
	.cfi_def_cfa_offset 16
	.cfi_offset 12, -16
	movl	$128, %esi
	leaq	.LC0(%rip), %r12
	pushq	%rbp
	.cfi_def_cfa_offset 24
	.cfi_offset 6, -24
	pushq	%rbx
	.cfi_def_cfa_offset 32
	.cfi_offset 3, -32
	subq	$144, %rsp
	.cfi_def_cfa_offset 176
	movq	stdin(%rip), %rdx
	movq	%fs:40, %rax
	movq	%rax, 136(%rsp)
	xorl	%eax, %eax
	movq	%rsp, %rbp
	movq	%rbp, %rdi
	call	fgets@PLT
	movq	%rbp, %rdi
	movq	%r12, %rsi
	call	strtok@PLT
	movl	$10, %edx
	xorl	%esi, %esi
	movq	%rax, %rdi
	call	strtol@PLT
	xorl	%edi, %edi
	movq	%r12, %rsi
	movq	%rax, %rbp
	movl	%eax, %ebx
	call	strtok@PLT
	xorl	%esi, %esi
	movl	$10, %edx
	movq	%rax, %rdi
	call	strtol@PLT
	orl	%eax, %ebp
	js	.L10
	movl	%eax, %edi
	xorl	%edx, %edx
	leal	1(%rax), %r8d
	.p2align 4,,10
	.p2align 3
.L3:
	testl	%edi, %edi
	js	.L4
	movl	%edi, %eax
	leal	1(%rdi), %esi
	jmp	.L5
	.p2align 4,,10
	.p2align 3
.L7:
	subl	$1, %eax
	jb	.L4
.L5:
	xorl	%ecx, %ecx
	cmpl	%eax, %ebx
	setge	%cl
	addl	%ecx, %edx
	movl	%esi, %ecx
	subl	%eax, %ecx
	cmpl	%ebx, %ecx
	jle	.L7
.L4:
	movl	%r8d, %eax
	subl	%edi, %eax
	cmpl	%eax, %ebx
	jl	.L2
	subl	$1, %edi
	jnb	.L3
.L2:
	xorl	%eax, %eax
	leaq	.LC1(%rip), %rsi
	movl	$1, %edi
	call	__printf_chk@PLT
	movq	136(%rsp), %rax
	subq	%fs:40, %rax
	jne	.L19
	addq	$144, %rsp
	.cfi_remember_state
	.cfi_def_cfa_offset 32
	xorl	%eax, %eax
	popq	%rbx
	.cfi_def_cfa_offset 24
	popq	%rbp
	.cfi_def_cfa_offset 16
	popq	%r12
	.cfi_def_cfa_offset 8
	ret
.L10:
	.cfi_restore_state
	xorl	%edx, %edx
	jmp	.L2
.L19:
	call	__stack_chk_fail@PLT
	.cfi_endproc
.LFE51:
	.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>
#include<stdlib.h>
#include<string.h>

int main(void) {
	int i;
	int K, S;
	int remaining;
	int x, y, z;
	int patterns;
	char buf[128], *ch;

	fgets(buf, sizeof(buf), stdin);
	ch = strtok(buf, " ");
	K = atoi(ch);
	ch = strtok(NULL, " ");
	S = atoi(ch);

	patterns = 0;
	for(x = 0; x <= K; x += 1) {
		remaining = S - x;
		if(remaining < 0) {
			break;
		}
		for(y = 0; y <= K; y += 1) {
			remaining = S - x - y;
			if(remaining < 0) {
				break;
			}
			if(remaining <= K) {
				patterns += 1;
			}
		}
	}

	printf("%d\n", patterns);

	return 0;
}

3 2
 5 7
 3 3
 4 7
 3 4
 1 7
 2 5
 4 0
 6 7
 17 4

6
 27
 10
 18
 12
 0
 3
 1
 33
 15

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>
#include<stdlib.h>
#include<string.h>

int main(void) {
	int i;
	int K, S;
	int remaining;
	int x, y, z;
	int patterns;
	char buf[128], *ch;

	fgets(buf, sizeof(buf), stdin);
	ch = strtok(buf, " ");
	K = atoi(ch);
	ch = strtok(NULL, " ");
	S = atoi(ch);

	patterns = 0;
	for(x = 0; x <= K; x += 1) {
		remaining = S - x;
		if(remaining < 0) {
			break;
		}
		for(y = 0; y <= K; y += 1) {
			remaining = S - x - y;
			if(remaining < 0) {
				break;
			}
			if(remaining <= K) {
				patterns += 1;
			}
		}
	}

	printf("%d\n", patterns);

	return 0;
}
```

Unoptimized Assembly Code:

```assembly
	.file	"temp.c"
	.text
	.section	.rodata
.LC0:
	.string	" "
.LC1:
	.string	"%d\n"
	.text
	.globl	main
	.type	main, @function
main:
.LFB6:
	.cfi_startproc
	endbr64
	pushq	%rbp
	.cfi_def_cfa_offset 16
	.cfi_offset 6, -16
	movq	%rsp, %rbp
	.cfi_def_cfa_register 6
	subq	$176, %rsp
	movq	%fs:40, %rax
	movq	%rax, -8(%rbp)
	xorl	%eax, %eax
	movq	stdin(%rip), %rdx
	leaq	-144(%rbp), %rax
	movl	$128, %esi
	movq	%rax, %rdi
	call	fgets@PLT
	leaq	-144(%rbp), %rax
	leaq	.LC0(%rip), %rdx
	movq	%rdx, %rsi
	movq	%rax, %rdi
	call	strtok@PLT
	movq	%rax, -152(%rbp)
	movq	-152(%rbp), %rax
	movq	%rax, %rdi
	call	atoi@PLT
	movl	%eax, -164(%rbp)
	leaq	.LC0(%rip), %rax
	movq	%rax, %rsi
	movl	$0, %edi
	call	strtok@PLT
	movq	%rax, -152(%rbp)
	movq	-152(%rbp), %rax
	movq	%rax, %rdi
	call	atoi@PLT
	movl	%eax, -160(%rbp)
	movl	$0, -168(%rbp)
	movl	$0, -176(%rbp)
	jmp	.L2
.L10:
	movl	-160(%rbp), %eax
	subl	-176(%rbp), %eax
	movl	%eax, -156(%rbp)
	cmpl	$0, -156(%rbp)
	js	.L13
	movl	$0, -172(%rbp)
	jmp	.L5
.L9:
	movl	-160(%rbp), %eax
	subl	-176(%rbp), %eax
	subl	-172(%rbp), %eax
	movl	%eax, -156(%rbp)
	cmpl	$0, -156(%rbp)
	js	.L14
	movl	-156(%rbp), %eax
	cmpl	-164(%rbp), %eax
	jg	.L8
	addl	$1, -168(%rbp)
.L8:
	addl	$1, -172(%rbp)
.L5:
	movl	-172(%rbp), %eax
	cmpl	-164(%rbp), %eax
	jle	.L9
	jmp	.L7
.L14:
	nop
.L7:
	addl	$1, -176(%rbp)
.L2:
	movl	-176(%rbp), %eax
	cmpl	-164(%rbp), %eax
	jle	.L10
	jmp	.L4
.L13:
	nop
.L4:
	movl	-168(%rbp), %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	.L12
	call	__stack_chk_fail@PLT
.L12:
	leave
	.cfi_def_cfa 7, 8
	ret
	.cfi_endproc
.LFE6:
	.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.
train
	.file	"temp.c"
	.text
	.section	.rodata
.LC0:
	.string	" "
.LC1:
	.string	"%d\n"
	.text
	.globl	main
	.type	main, @function
main:
.LFB6:
	.cfi_startproc
	endbr64
	pushq	%rbp
	.cfi_def_cfa_offset 16
	.cfi_offset 6, -16
	movq	%rsp, %rbp
	.cfi_def_cfa_register 6
	subq	$176, %rsp
	movq	%fs:40, %rax
	movq	%rax, -8(%rbp)
	xorl	%eax, %eax
	movq	stdin(%rip), %rdx
	leaq	-144(%rbp), %rax
	movl	$128, %esi
	movq	%rax, %rdi
	call	fgets@PLT
	leaq	-144(%rbp), %rax
	leaq	.LC0(%rip), %rdx
	movq	%rdx, %rsi
	movq	%rax, %rdi
	call	strtok@PLT
	movq	%rax, -152(%rbp)
	movq	-152(%rbp), %rax
	movq	%rax, %rdi
	call	atoi@PLT
	movl	%eax, -164(%rbp)
	leaq	.LC0(%rip), %rax
	movq	%rax, %rsi
	movl	$0, %edi
	call	strtok@PLT
	movq	%rax, -152(%rbp)
	movq	-152(%rbp), %rax
	movq	%rax, %rdi
	call	atoi@PLT
	movl	%eax, -160(%rbp)
	movl	$0, -168(%rbp)
	movl	$0, -176(%rbp)
	jmp	.L2
.L10:
	movl	-160(%rbp), %eax
	subl	-176(%rbp), %eax
	movl	%eax, -156(%rbp)
	cmpl	$0, -156(%rbp)
	js	.L13
	movl	$0, -172(%rbp)
	jmp	.L5
.L9:
	movl	-160(%rbp), %eax
	subl	-176(%rbp), %eax
	subl	-172(%rbp), %eax
	movl	%eax, -156(%rbp)
	cmpl	$0, -156(%rbp)
	js	.L14
	movl	-156(%rbp), %eax
	cmpl	-164(%rbp), %eax
	jg	.L8
	addl	$1, -168(%rbp)
.L8:
	addl	$1, -172(%rbp)
.L5:
	movl	-172(%rbp), %eax
	cmpl	-164(%rbp), %eax
	jle	.L9
	jmp	.L7
.L14:
	nop
.L7:
	addl	$1, -176(%rbp)
.L2:
	movl	-176(%rbp), %eax
	cmpl	-164(%rbp), %eax
	jle	.L10
	jmp	.L4
.L13:
	nop
.L4:
	movl	-168(%rbp), %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	.L12
	call	__stack_chk_fail@PLT
.L12:
	leave
	.cfi_def_cfa 7, 8
	ret
	.cfi_endproc
.LFE6:
	.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:
