#D5676. Positions in Permutations
Positions in Permutations
Positions in Permutations
Permutation p is an ordered set of integers p1, p2, ..., pn, consisting of n distinct positive integers, each of them doesn't exceed n. We'll denote the i-th element of permutation p as pi. We'll call number n the size or the length of permutation p1, p2, ..., pn.
We'll call position i (1 ≤ i ≤ n) in permutation p1, p2, ..., pn 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, 2, 3) — 0 positions
- — 2 positions
- — 2 positions
- — 2 positions
- — 2 positions
- (3, 2, 1) — 0 positions
inputFormat
Input
The single line contains two space-separated integers n and k (1 ≤ n ≤ 1000, 0 ≤ k ≤ n).
outputFormat
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, 2, 3) — 0 positions
- — 2 positions
- — 2 positions
- — 2 positions
- — 2 positions
- (3, 2, 1) — 0 positions
样例
2 1
0