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Positions in Permutations

2000ms 262144K

Description:

Permutation 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).

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).

Sample Input:

1 0

Sample Output:

1

Sample Input:

2 1

Sample Output:

0

Sample Input:

3 2

Sample Output:

4

Sample Input:

4 1

Sample Output:

6

Sample Input:

7 4

Sample Output:

328

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

Informação

Codeforces

Provedor Codeforces

Código CF285E

Tags

combinatoricsdpmath

Submetido 0

BOUA! 0

Taxa de BOUA's 0%

Datas 09/05/2023 08:42:50

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