Permutation p is an ordered set of integers p_1,  p_2,  ...,  p_{n}, consisting of n distinct positive integers, each of them doesn't exceed n. We'll denote the i-th element of permutation p as p_{i}. We'll call number n the size or the length of permutation p_1,  p_2,  ...,  p_{n}.

We'll call position i (1 ≤ i ≤ n) in permutation p_1, p_2, ..., p_{n} good, if |p[i] - i| = 1. Count the number of permutations of size n with exactly k good positions. Print the answer modulo 1000000007 (10^9 + 7).


-----Input-----

The single line contains two space-separated integers n and k (1 ≤ n ≤ 1000, 0 ≤ k ≤ n).


-----Output-----

Print the number of permutations of length n with exactly k good positions modulo 1000000007 (10^9 + 7).


-----Examples-----
Input
1 0

Output
1

Input
2 1

Output
0

Input
3 2

Output
4

Input
4 1

Output
6

Input
7 4

Output
328



-----Note-----

The only permutation of size 1 has 0 good positions.

Permutation (1, 2) has 0 good positions, and permutation (2, 1) has 2 positions.

Permutations of size 3:



 (1, 2, 3) — 0 positions

 $(1,3,2)$ — 2 positions

 $(2,1,3)$ — 2 positions

 $(2,3,1)$ — 2 positions

 $(3,1,2)$ — 2 positions

 (3, 2, 1) — 0 positions

Difficulty: interview

Starter code:

Solutions:
mod=10**9+7
n,k=list(map(int,input().split()))

A=[0]*(n+1)
B=[0]*(n+1)
C=[0]*(n+1)
F=[0]*(n+1)
G=[0]*(n+1)

F[0]=G[0]=1
for i in range(1,n+1):
	G[i]=F[i]=F[i-1]*i%mod
	G[i]=pow(F[i],(mod-2),mod)

for i in range(0,n):
	if i*2>n:
		break
	B[i]=(F[n-i]*G[i]*G[n-i*2])%mod
for i in range(0,n//2+1):
	for j in range(0,n//2+1):
		A[i+j]=(A[i+j]+B[i]*B[j])%mod
for i in range(0,n+1):
	A[i]=A[i]*F[n-i]%mod
for i in range(0,n+1):
	for j in range(0,i+1):
		C[j]=(C[j]+A[i]*F[i]*G[j]*G[i-j]*(1-(i-j)%2*2))%mod
print(C[k]%mod)


# METO Bot 0.9.9
mod=10**9+7
n,k=list(map(int,input().split()))

A=[0]*(n+1)
B=[0]*(n+1)
C=[0]*(n+1)
F=[0]*(n+1)
G=[0]*(n+1)

F[0]=G[0]=1
for i in range(1,n+1):
	G[i]=F[i]=F[i-1]*i%mod
	G[i]=pow(F[i],(mod-2),mod)

for i in range(0,n):
	if i*2>n:
		break
	B[i]=(F[n-i]*G[i]*G[n-i*2])%mod
for i in range(0,n//2+1):
	for j in range(0,n//2+1):
		A[i+j]=(A[i+j]+B[i]*B[j])%mod
for i in range(0,n+1):
	A[i]=A[i]*F[n-i]%mod
for i in range(0,n+1):
	for j in range(0,i+1):
		C[j]=(C[j]+A[i]*F[i]*G[j]*G[i-j]*(1-(i-j)%2*2))%mod
print(C[k]%mod)



mod=10**9+7
n,k=list(map(int,input().split()))

A=[0]*(n+1)
B=[0]*(n+1)
C=[0]*(n+1)
F=[0]*(n+1)
G=[0]*(n+1)

F[0]=G[0]=1
for i in range(1,n+1):
	G[i]=F[i]=F[i-1]*i%mod
	G[i]=pow(F[i],(mod-2),mod)

for i in range(0,n):
	if i*2>n:
		break
	B[i]=(F[n-i]*G[i]*G[n-i*2])%mod
for i in range(0,n//2+1):
	for j in range(0,n//2+1):
		A[i+j]=(A[i+j]+B[i]*B[j])%mod
for i in range(0,n+1):
	A[i]=A[i]*F[n-i]%mod
for i in range(0,n+1):
	for j in range(0,i+1):
		C[j]=(C[j]+A[i]*F[i]*G[j]*G[i-j]*(1-(i-j)%2*2))%mod
print(C[k]%mod)



mod=10**9+7
n,k=list(map(int,input().split()))

A=[0]*(n+1)
B=[0]*(n+1)
C=[0]*(n+1)
F=[0]*(n+1)
G=[0]*(n+1)

F[0]=G[0]=1
for i in range(1,n+1):
	G[i]=F[i]=F[i-1]*i%mod
	G[i]=pow(F[i],(mod-2),mod)

for i in range(0,n):
	if i*2>n:
		break
	B[i]=(F[n-i]*G[i]*G[n-i*2])%mod
for i in range(0,n//2+1):
	for j in range(0,n//2+1):
		A[i+j]=(A[i+j]+B[i]*B[j])%mod
for i in range(0,n+1):
	A[i]=A[i]*F[n-i]%mod
for i in range(0,n+1):
	for j in range(0,i+1):
		C[j]=(C[j]+A[i]*F[i]*G[j]*G[i-j]*(1-(i-j)%2*2))%mod
print(C[k]%mod)



mod=10**9+7
n,k=list(map(int,input().split()))

A=[0]*(n+1)
B=[0]*(n+1)
C=[0]*(n+1)
F=[0]*(n+1)
G=[0]*(n+1)

F[0]=G[0]=1
for i in range(1,n+1):
	G[i]=F[i]=F[i-1]*i%mod
	G[i]=pow(F[i],(mod-2),mod)

for i in range(0,n):
	if i*2>n:
		break
	B[i]=(F[n-i]*G[i]*G[n-i*2])%mod
for i in range(0,n//2+1):
	for j in range(0,n//2+1):
		A[i+j]=(A[i+j]+B[i]*B[j])%mod
for i in range(0,n+1):
	A[i]=A[i]*F[n-i]%mod
for i in range(0,n+1):
	for j in range(0,i+1):
		C[j]=(C[j]+A[i]*F[i]*G[j]*G[i-j]*(1-(i-j)%2*2))%mod
print(C[k]%mod)



mod=10**9+7
n,k=list(map(int,input().split()))

A=[0]*(n+1)
B=[0]*(n+1)
C=[0]*(n+1)
F=[0]*(n+1)
G=[0]*(n+1)

F[0]=G[0]=1
for i in range(1,n+1):
	G[i]=F[i]=F[i-1]*i%mod
	G[i]=pow(F[i],(mod-2),mod)

for i in range(0,n):
	if i*2>n:
		break
	B[i]=(F[n-i]*G[i]*G[n-i*2])%mod
for i in range(0,n//2+1):
	for j in range(0,n//2+1):
		A[i+j]=(A[i+j]+B[i]*B[j])%mod
for i in range(0,n+1):
	A[i]=A[i]*F[n-i]%mod
for i in range(0,n+1):
	for j in range(0,i+1):
		C[j]=(C[j]+A[i]*F[i]*G[j]*G[i-j]*(1-(i-j)%2*2))%mod
print(C[k]%mod)



mod=10**9+7
n,k=list(map(int,input().split()))

A=[0]*(n+1)
B=[0]*(n+1)
C=[0]*(n+1)
F=[0]*(n+1)
G=[0]*(n+1)

F[0]=G[0]=1
for i in range(1,n+1):
	G[i]=F[i]=F[i-1]*i%mod
	G[i]=pow(F[i],(mod-2),mod)

for i in range(0,n):
	if i*2>n:
		break
	B[i]=(F[n-i]*G[i]*G[n-i*2])%mod
for i in range(0,n//2+1):
	for j in range(0,n//2+1):
		A[i+j]=(A[i+j]+B[i]*B[j])%mod
for i in range(0,n+1):
	A[i]=A[i]*F[n-i]%mod
for i in range(0,n+1):
	for j in range(0,i+1):
		C[j]=(C[j]+A[i]*F[i]*G[j]*G[i-j]*(1-(i-j)%2*2))%mod
print(C[k]%mod)



mod=10**9+7
n,k=list(map(int,input().split()))

A=[0]*(n+1)
B=[0]*(n+1)
C=[0]*(n+1)
F=[0]*(n+1)
G=[0]*(n+1)

F[0]=G[0]=1
for i in range(1,n+1):
	G[i]=F[i]=F[i-1]*i%mod
	G[i]=pow(F[i],(mod-2),mod)

for i in range(0,n):
	if i*2>n:
		break
	B[i]=(F[n-i]*G[i]*G[n-i*2])%mod
for i in range(0,n//2+1):
	for j in range(0,n//2+1):
		A[i+j]=(A[i+j]+B[i]*B[j])%mod
for i in range(0,n+1):
	A[i]=A[i]*F[n-i]%mod
for i in range(0,n+1):
	for j in range(0,i+1):
		C[j]=(C[j]+A[i]*F[i]*G[j]*G[i-j]*(1-(i-j)%2*2))%mod
print(C[k]%mod)



mod=10**9+7
n,k=list(map(int,input().split()))

A=[0]*(n+1)
B=[0]*(n+1)
C=[0]*(n+1)
F=[0]*(n+1)
G=[0]*(n+1)

F[0]=G[0]=1
for i in range(1,n+1):
	G[i]=F[i]=F[i-1]*i%mod
	G[i]=pow(F[i],(mod-2),mod)

for i in range(0,n):
	if i*2>n:
		break
	B[i]=(F[n-i]*G[i]*G[n-i*2])%mod
for i in range(0,n//2+1):
	for j in range(0,n//2+1):
		A[i+j]=(A[i+j]+B[i]*B[j])%mod
for i in range(0,n+1):
	A[i]=A[i]*F[n-i]%mod
for i in range(0,n+1):
	for j in range(0,i+1):
		C[j]=(C[j]+A[i]*F[i]*G[j]*G[i-j]*(1-(i-j)%2*2))%mod
print(C[k]%mod)