Permutations and cycles

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 $2 \le n \le 1000$ and $1 \le k \le \lfloor n/2 \rfloor$ .

Output

For every case, print $f(n, k)$ . Because that number can become very large, use @long long@’s and make the computations modulo $10^9 + 7$ .

Hint

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

Problem information

Author: Unknown
Translator: Salvador Roura

Generation: 2026-01-25T12:22:16.426Z