CF285E Positions in Permutations

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

The single line contains two space-separated integers $ n $ and $ k $ ( $ 1

Print the number of permutations of length $ n $ with exactly $ k $ good positions modulo $ 1000000007 $ ( $ 10^{9}+7 $ ).

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. $ (1,2,3) $ — 0 positions 2.  — 2 positions 3.  — 2 positions 4.  — 2 positions 5.  — 2 positions 6. $ (3,2,1) $ — 0 positions