Please, try EDU on Codeforces! New educational section with videos, subtitles, texts, and problems. ×

E. Positions in Permutations
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

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 (109 + 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 (109 + 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. (1, 2, 3) — 0 positions
2. — 2 positions
3. — 2 positions
4. — 2 positions
5. — 2 positions
6. (3, 2, 1) — 0 positions