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Permutation counting - MarisaOJ: Marisa Online Judge

Permutation counting

Time limit: 1000 ms
Memory limit: 256 MB

Count the number of permutations of integers from $1$ to $n$ that $|p_i-i| \le m$.

Input

  • A single line contains two integers $n,k$.

Output

  • Print the number of permutations modulo $10^9+7$.

Constraints

  • $1 \le n \le 1000$.
  • $1 \le k \le 6$.

Example

Input:

4 2

Output:

14