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