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 $1000000007$ ($10^{9} + 7$).

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. $(1, 2, 3)$ — 0 positions
2. — 2 positions
3. — 2 positions
4. — 2 positions
5. — 2 positions
6. $(3, 2, 1)$ — 0 positions