Permutations and cycles P99557

Given two natural numbers n and k, let f(n, k) denote the number of permutations with n ‍elements, and such that there are exactly k ‍cycles, all them of length at least 2. Implement a dynamic programming code to compute f(n, k).

Input

Input consists of several cases, each with two natural numbers n and k. You can assume 2 ≤ n ≤ 1000 and 1 ≤ k ≤ ⌊ n/2 ⌋.

Output

For every case, print f(n, k). Because that number can become very large, use long long’s and make the computations modulo 10⁹ + 7.

Hint

You can compute f(n, k) just adding two “recursive calls”.