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 n,k,i,m=1e9+7;
long a[200001]={},r=0;
int main(){
    scanf("%d%d",&n,&k);
    for(i=1;i<=n+1;i++)a[i]=(a[i-1]+i)%m;
    for(i=k;i<=n+1;i++)r=(r+(a[n]+1+m-a[n-i<0?0:n-i]-a[i-1]))%m;
    printf("%ld",r);
    return 0;
}```

Unoptimized Assembly Code:

```assembly
	.file	"temp.c"
	.text
	.globl	n
	.bss
	.align 4
	.type	n, @object
	.size	n, 4
n:
	.zero	4
	.globl	k
	.align 4
	.type	k, @object
	.size	k, 4
k:
	.zero	4
	.globl	i
	.align 4
	.type	i, @object
	.size	i, 4
i:
	.zero	4
	.globl	m
	.data
	.align 4
	.type	m, @object
	.size	m, 4
m:
	.long	1000000007
	.globl	a
	.bss
	.align 32
	.type	a, @object
	.size	a, 1600008
a:
	.zero	1600008
	.globl	r
	.align 8
	.type	r, @object
	.size	r, 8
r:
	.zero	8
	.section	.rodata
.LC0:
	.string	"%d%d"
.LC1:
	.string	"%ld"
	.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
	leaq	k(%rip), %rax
	movq	%rax, %rdx
	leaq	n(%rip), %rax
	movq	%rax, %rsi
	leaq	.LC0(%rip), %rax
	movq	%rax, %rdi
	movl	$0, %eax
	call	__isoc99_scanf@PLT
	movl	$1, i(%rip)
	jmp	.L2
.L3:
	movl	i(%rip), %eax
	subl	$1, %eax
	cltq
	leaq	0(,%rax,8), %rdx
	leaq	a(%rip), %rax
	movq	(%rdx,%rax), %rdx
	movl	i(%rip), %eax
	cltq
	addq	%rdx, %rax
	movl	m(%rip), %edx
	movslq	%edx, %rsi
	movl	i(%rip), %ecx
	cqto
	idivq	%rsi
	movq	%rdx, %rsi
	movslq	%ecx, %rax
	leaq	0(,%rax,8), %rdx
	leaq	a(%rip), %rax
	movq	%rsi, (%rdx,%rax)
	movl	i(%rip), %eax
	addl	$1, %eax
	movl	%eax, i(%rip)
.L2:
	movl	n(%rip), %eax
	leal	1(%rax), %edx
	movl	i(%rip), %eax
	cmpl	%eax, %edx
	jge	.L3
	movl	k(%rip), %eax
	movl	%eax, i(%rip)
	jmp	.L4
.L5:
	movl	n(%rip), %eax
	cltq
	leaq	0(,%rax,8), %rdx
	leaq	a(%rip), %rax
	movq	(%rdx,%rax), %rax
	leaq	1(%rax), %rdx
	movl	m(%rip), %eax
	cltq
	leaq	(%rdx,%rax), %rcx
	movl	n(%rip), %eax
	movl	i(%rip), %edx
	subl	%edx, %eax
	movl	$0, %edx
	testl	%eax, %eax
	cmovs	%edx, %eax
	cltq
	leaq	0(,%rax,8), %rdx
	leaq	a(%rip), %rax
	movq	(%rdx,%rax), %rax
	subq	%rax, %rcx
	movl	i(%rip), %eax
	subl	$1, %eax
	cltq
	leaq	0(,%rax,8), %rdx
	leaq	a(%rip), %rax
	movq	(%rdx,%rax), %rax
	subq	%rax, %rcx
	movq	%rcx, %rdx
	movq	r(%rip), %rax
	addq	%rdx, %rax
	movl	m(%rip), %edx
	movslq	%edx, %rcx
	cqto
	idivq	%rcx
	movq	%rdx, %rax
	movq	%rax, r(%rip)
	movl	i(%rip), %eax
	addl	$1, %eax
	movl	%eax, i(%rip)
.L4:
	movl	n(%rip), %eax
	leal	1(%rax), %edx
	movl	i(%rip), %eax
	cmpl	%eax, %edx
	jge	.L5
	movq	r(%rip), %rax
	movq	%rax, %rsi
	leaq	.LC1(%rip), %rax
	movq	%rax, %rdi
	movl	$0, %eax
	call	printf@PLT
	movl	$0, %eax
	popq	%rbp
	.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"
.LC1:
	.string	"%ld"
	.section	.text.startup,"ax",@progbits
	.p2align 4
	.globl	main
	.type	main, @function
main:
.LFB23:
	.cfi_startproc
	endbr64
	leaq	.LC0(%rip), %rdi
	subq	$8, %rsp
	.cfi_def_cfa_offset 16
	leaq	k(%rip), %rdx
	xorl	%eax, %eax
	leaq	n(%rip), %rsi
	call	__isoc99_scanf@PLT
	movl	n(%rip), %edi
	leal	1(%rdi), %r10d
	testl	%r10d, %r10d
	jle	.L2
	movl	%edi, %r9d
	movslq	m(%rip), %r8
	movq	a(%rip), %rdx
	movl	$1, %ecx
	addq	$2, %r9
	leaq	a(%rip), %rsi
	.p2align 4,,10
	.p2align 3
.L3:
	leaq	(%rcx,%rdx), %rax
	cqto
	idivq	%r8
	movq	%rdx, (%rsi,%rcx,8)
	addq	$1, %rcx
	cmpq	%rcx, %r9
	jne	.L3
.L2:
	movslq	k(%rip), %rax
	movq	r(%rip), %rdx
	movl	%eax, i(%rip)
	cmpl	%r10d, %eax
	jg	.L4
	leaq	a(%rip), %rsi
	movslq	%edi, %rcx
	movslq	m(%rip), %r9
	movq	(%rsi,%rcx,8), %rcx
	leaq	-8(%rsi,%rax,8), %r8
	leaq	1(%r9,%rcx), %r10
	movl	%edi, %ecx
	subl	%eax, %ecx
	.p2align 4,,10
	.p2align 3
.L5:
	xorl	%eax, %eax
	testl	%ecx, %ecx
	movq	%r10, %r11
	cmovns	%ecx, %eax
	subl	$1, %ecx
	addq	$8, %r8
	cltq
	subq	(%rsi,%rax,8), %r11
	movq	%r11, %rax
	subq	-8(%r8), %rax
	addq	%rdx, %rax
	cqto
	idivq	%r9
	cmpl	$-2, %ecx
	jne	.L5
	addl	$2, %edi
	movq	%rdx, r(%rip)
	movl	%edi, i(%rip)
.L4:
	leaq	.LC1(%rip), %rsi
	movl	$1, %edi
	xorl	%eax, %eax
	call	__printf_chk@PLT
	xorl	%eax, %eax
	addq	$8, %rsp
	.cfi_def_cfa_offset 8
	ret
	.cfi_endproc
.LFE23:
	.size	main, .-main
	.globl	r
	.bss
	.align 8
	.type	r, @object
	.size	r, 8
r:
	.zero	8
	.globl	a
	.align 32
	.type	a, @object
	.size	a, 1600008
a:
	.zero	1600008
	.globl	m
	.data
	.align 4
	.type	m, @object
	.size	m, 4
m:
	.long	1000000007
	.globl	i
	.bss
	.align 4
	.type	i, @object
	.size	i, 4
i:
	.zero	4
	.globl	k
	.align 4
	.type	k, @object
	.size	k, 4
k:
	.zero	4
	.globl	n
	.align 4
	.type	n, @object
	.size	n, 4
n:
	.zero	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
	.file	"temp.c"
	.text
	.section	.rodata.str1.1,"aMS",@progbits,1
.LC0:
	.string	"%d%d"
.LC1:
	.string	"%ld"
	.section	.text.startup,"ax",@progbits
	.p2align 4
	.globl	main
	.type	main, @function
main:
.LFB23:
	.cfi_startproc
	endbr64
	leaq	.LC0(%rip), %rdi
	subq	$8, %rsp
	.cfi_def_cfa_offset 16
	leaq	k(%rip), %rdx
	xorl	%eax, %eax
	leaq	n(%rip), %rsi
	call	__isoc99_scanf@PLT
	movl	n(%rip), %edi
	leal	1(%rdi), %r10d
	testl	%r10d, %r10d
	jle	.L2
	movl	%edi, %r9d
	movslq	m(%rip), %r8
	movq	a(%rip), %rdx
	movl	$1, %ecx
	addq	$2, %r9
	leaq	a(%rip), %rsi
	.p2align 4,,10
	.p2align 3
.L3:
	leaq	(%rcx,%rdx), %rax
	cqto
	idivq	%r8
	movq	%rdx, (%rsi,%rcx,8)
	addq	$1, %rcx
	cmpq	%rcx, %r9
	jne	.L3
.L2:
	movslq	k(%rip), %rax
	movq	r(%rip), %rdx
	movl	%eax, i(%rip)
	cmpl	%r10d, %eax
	jg	.L4
	leaq	a(%rip), %rsi
	movslq	%edi, %rcx
	movslq	m(%rip), %r9
	movq	(%rsi,%rcx,8), %rcx
	leaq	-8(%rsi,%rax,8), %r8
	leaq	1(%r9,%rcx), %r10
	movl	%edi, %ecx
	subl	%eax, %ecx
	.p2align 4,,10
	.p2align 3
.L5:
	xorl	%eax, %eax
	testl	%ecx, %ecx
	movq	%r10, %r11
	cmovns	%ecx, %eax
	subl	$1, %ecx
	addq	$8, %r8
	cltq
	subq	(%rsi,%rax,8), %r11
	movq	%r11, %rax
	subq	-8(%r8), %rax
	addq	%rdx, %rax
	cqto
	idivq	%r9
	cmpl	$-2, %ecx
	jne	.L5
	addl	$2, %edi
	movq	%rdx, r(%rip)
	movl	%edi, i(%rip)
.L4:
	leaq	.LC1(%rip), %rsi
	movl	$1, %edi
	xorl	%eax, %eax
	call	__printf_chk@PLT
	xorl	%eax, %eax
	addq	$8, %rsp
	.cfi_def_cfa_offset 8
	ret
	.cfi_endproc
.LFE23:
	.size	main, .-main
	.globl	r
	.bss
	.align 8
	.type	r, @object
	.size	r, 8
r:
	.zero	8
	.globl	a
	.align 32
	.type	a, @object
	.size	a, 1600008
a:
	.zero	1600008
	.globl	m
	.data
	.align 4
	.type	m, @object
	.size	m, 4
m:
	.long	1000000007
	.globl	i
	.bss
	.align 4
	.type	i, @object
	.size	i, 4
i:
	.zero	4
	.globl	k
	.align 4
	.type	k, @object
	.size	k, 4
k:
	.zero	4
	.globl	n
	.align 4
	.type	n, @object
	.size	n, 4
n:
	.zero	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:

#include<stdio.h>
int n,k,i,m=1e9+7;
long a[200001]={},r=0;
int main(){
    scanf("%d%d",&n,&k);
    for(i=1;i<=n+1;i++)a[i]=(a[i-1]+i)%m;
    for(i=k;i<=n+1;i++)r=(r+(a[n]+1+m-a[n-i<0?0:n-i]-a[i-1]))%m;
    printf("%ld",r);
    return 0;
}
141421 60408

832536804
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 n,k,i,m=1e9+7;
long a[200001]={},r=0;
int main(){
    scanf("%d%d",&n,&k);
    for(i=1;i<=n+1;i++)a[i]=(a[i-1]+i)%m;
    for(i=k;i<=n+1;i++)r=(r+(a[n]+1+m-a[n-i<0?0:n-i]-a[i-1]))%m;
    printf("%ld",r);
    return 0;
}```

Unoptimized Assembly Code:

```assembly
	.file	"temp.c"
	.text
	.globl	n
	.bss
	.align 4
	.type	n, @object
	.size	n, 4
n:
	.zero	4
	.globl	k
	.align 4
	.type	k, @object
	.size	k, 4
k:
	.zero	4
	.globl	i
	.align 4
	.type	i, @object
	.size	i, 4
i:
	.zero	4
	.globl	m
	.data
	.align 4
	.type	m, @object
	.size	m, 4
m:
	.long	1000000007
	.globl	a
	.bss
	.align 32
	.type	a, @object
	.size	a, 1600008
a:
	.zero	1600008
	.globl	r
	.align 8
	.type	r, @object
	.size	r, 8
r:
	.zero	8
	.section	.rodata
.LC0:
	.string	"%d%d"
.LC1:
	.string	"%ld"
	.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
	leaq	k(%rip), %rax
	movq	%rax, %rdx
	leaq	n(%rip), %rax
	movq	%rax, %rsi
	leaq	.LC0(%rip), %rax
	movq	%rax, %rdi
	movl	$0, %eax
	call	__isoc99_scanf@PLT
	movl	$1, i(%rip)
	jmp	.L2
.L3:
	movl	i(%rip), %eax
	subl	$1, %eax
	cltq
	leaq	0(,%rax,8), %rdx
	leaq	a(%rip), %rax
	movq	(%rdx,%rax), %rdx
	movl	i(%rip), %eax
	cltq
	addq	%rdx, %rax
	movl	m(%rip), %edx
	movslq	%edx, %rsi
	movl	i(%rip), %ecx
	cqto
	idivq	%rsi
	movq	%rdx, %rsi
	movslq	%ecx, %rax
	leaq	0(,%rax,8), %rdx
	leaq	a(%rip), %rax
	movq	%rsi, (%rdx,%rax)
	movl	i(%rip), %eax
	addl	$1, %eax
	movl	%eax, i(%rip)
.L2:
	movl	n(%rip), %eax
	leal	1(%rax), %edx
	movl	i(%rip), %eax
	cmpl	%eax, %edx
	jge	.L3
	movl	k(%rip), %eax
	movl	%eax, i(%rip)
	jmp	.L4
.L5:
	movl	n(%rip), %eax
	cltq
	leaq	0(,%rax,8), %rdx
	leaq	a(%rip), %rax
	movq	(%rdx,%rax), %rax
	leaq	1(%rax), %rdx
	movl	m(%rip), %eax
	cltq
	leaq	(%rdx,%rax), %rcx
	movl	n(%rip), %eax
	movl	i(%rip), %edx
	subl	%edx, %eax
	movl	$0, %edx
	testl	%eax, %eax
	cmovs	%edx, %eax
	cltq
	leaq	0(,%rax,8), %rdx
	leaq	a(%rip), %rax
	movq	(%rdx,%rax), %rax
	subq	%rax, %rcx
	movl	i(%rip), %eax
	subl	$1, %eax
	cltq
	leaq	0(,%rax,8), %rdx
	leaq	a(%rip), %rax
	movq	(%rdx,%rax), %rax
	subq	%rax, %rcx
	movq	%rcx, %rdx
	movq	r(%rip), %rax
	addq	%rdx, %rax
	movl	m(%rip), %edx
	movslq	%edx, %rcx
	cqto
	idivq	%rcx
	movq	%rdx, %rax
	movq	%rax, r(%rip)
	movl	i(%rip), %eax
	addl	$1, %eax
	movl	%eax, i(%rip)
.L4:
	movl	n(%rip), %eax
	leal	1(%rax), %edx
	movl	i(%rip), %eax
	cmpl	%eax, %edx
	jge	.L5
	movq	r(%rip), %rax
	movq	%rax, %rsi
	leaq	.LC1(%rip), %rax
	movq	%rax, %rdi
	movl	$0, %eax
	call	printf@PLT
	movl	$0, %eax
	popq	%rbp
	.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.
train
	.file	"temp.c"
	.text
	.globl	n
	.bss
	.align 4
	.type	n, @object
	.size	n, 4
n:
	.zero	4
	.globl	k
	.align 4
	.type	k, @object
	.size	k, 4
k:
	.zero	4
	.globl	i
	.align 4
	.type	i, @object
	.size	i, 4
i:
	.zero	4
	.globl	m
	.data
	.align 4
	.type	m, @object
	.size	m, 4
m:
	.long	1000000007
	.globl	a
	.bss
	.align 32
	.type	a, @object
	.size	a, 1600008
a:
	.zero	1600008
	.globl	r
	.align 8
	.type	r, @object
	.size	r, 8
r:
	.zero	8
	.section	.rodata
.LC0:
	.string	"%d%d"
.LC1:
	.string	"%ld"
	.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
	leaq	k(%rip), %rax
	movq	%rax, %rdx
	leaq	n(%rip), %rax
	movq	%rax, %rsi
	leaq	.LC0(%rip), %rax
	movq	%rax, %rdi
	movl	$0, %eax
	call	__isoc99_scanf@PLT
	movl	$1, i(%rip)
	jmp	.L2
.L3:
	movl	i(%rip), %eax
	subl	$1, %eax
	cltq
	leaq	0(,%rax,8), %rdx
	leaq	a(%rip), %rax
	movq	(%rdx,%rax), %rdx
	movl	i(%rip), %eax
	cltq
	addq	%rdx, %rax
	movl	m(%rip), %edx
	movslq	%edx, %rsi
	movl	i(%rip), %ecx
	cqto
	idivq	%rsi
	movq	%rdx, %rsi
	movslq	%ecx, %rax
	leaq	0(,%rax,8), %rdx
	leaq	a(%rip), %rax
	movq	%rsi, (%rdx,%rax)
	movl	i(%rip), %eax
	addl	$1, %eax
	movl	%eax, i(%rip)
.L2:
	movl	n(%rip), %eax
	leal	1(%rax), %edx
	movl	i(%rip), %eax
	cmpl	%eax, %edx
	jge	.L3
	movl	k(%rip), %eax
	movl	%eax, i(%rip)
	jmp	.L4
.L5:
	movl	n(%rip), %eax
	cltq
	leaq	0(,%rax,8), %rdx
	leaq	a(%rip), %rax
	movq	(%rdx,%rax), %rax
	leaq	1(%rax), %rdx
	movl	m(%rip), %eax
	cltq
	leaq	(%rdx,%rax), %rcx
	movl	n(%rip), %eax
	movl	i(%rip), %edx
	subl	%edx, %eax
	movl	$0, %edx
	testl	%eax, %eax
	cmovs	%edx, %eax
	cltq
	leaq	0(,%rax,8), %rdx
	leaq	a(%rip), %rax
	movq	(%rdx,%rax), %rax
	subq	%rax, %rcx
	movl	i(%rip), %eax
	subl	$1, %eax
	cltq
	leaq	0(,%rax,8), %rdx
	leaq	a(%rip), %rax
	movq	(%rdx,%rax), %rax
	subq	%rax, %rcx
	movq	%rcx, %rdx
	movq	r(%rip), %rax
	addq	%rdx, %rax
	movl	m(%rip), %edx
	movslq	%edx, %rcx
	cqto
	idivq	%rcx
	movq	%rdx, %rax
	movq	%rax, r(%rip)
	movl	i(%rip), %eax
	addl	$1, %eax
	movl	%eax, i(%rip)
.L4:
	movl	n(%rip), %eax
	leal	1(%rax), %edx
	movl	i(%rip), %eax
	cmpl	%eax, %edx
	jge	.L5
	movq	r(%rip), %rax
	movq	%rax, %rsi
	leaq	.LC1(%rip), %rax
	movq	%rax, %rdi
	movl	$0, %eax
	call	printf@PLT
	movl	$0, %eax
	popq	%rbp
	.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:
