Permutation p is an ordered set of integers p₁, p₂, ..., 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 p₁, p₂, ..., p_n.

We'll call position i (1 ≤ i ≤ n) in permutation p₁, p₂, ..., 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).

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
$\text{[math]}$ — 2 positions
$\text{[math]}$ — 2 positions
$\text{[math]}$ — 2 positions
$\text{[math]}$ — 2 positions
(3, 2, 1) — 0 positions

Positions in Permutations

Examples