E. Positions in Permutationstime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputPermutation 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).InputThe single line contains two space-separated integers n and k (1 ≤ n ≤ 1000, 0 ≤ k ≤ n).OutputPrint the number of permutations of length n with exactly k good positions modulo 1000000007 (109 + 7).ExamplesInput1 0Output1Input2 1Output0Input3 2Output4Input4 1Output6Input7 4Output328NoteThe 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
Input1 0
Output1
['combinatorics', 'dp', 'math', '*2600']