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).

Examples

Input

1 0


Output

1


Input

2 1


Output

0


Input

3 2


Output

4


Input

4 1


Output

6


Input

7 4


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. <image> — 2 positions
  3. <image> — 2 positions
  4. <image> — 2 positions
  5. <image> — 2 positions
  6. (3, 2, 1) — 0 positions
#include <bits/stdc++.h>
using namespace std;
const int MAXN = 1010;
long long f[MAXN][MAXN][3][2];
int n, m;
const int mod = 1e9 + 7;
int main() {
  cin >> n >> m;
  f[1][0][2][0] = 1;
  f[2][0][2][0] = 1;
  f[2][2][1][1] = 1;
  f[3][0][0][0] = 1;
  f[3][0][2][0] = 1;
  f[3][2][0][1] = 1;
  f[3][2][1][0] = 1;
  f[3][2][1][1] = 1;
  f[3][2][2][0] = 1;
  for (int i = 3; i <= n; i++) {
    for (int j = 0; j <= i; j++) {
      f[i + 1][j][2][0] = (f[i + 1][j][2][0] % mod + f[i][j][0][0] % mod) % mod;
      f[i + 1][j][0][0] = (f[i + 1][j][0][0] % mod +
                           (max((i - 2 - j), 0) * f[i][j][0][0]) % mod) %
                          mod;
      if (j - 1 >= 0)
        f[i + 1][j - 1][0][0] =
            (f[i + 1][j - 1][0][0] % mod + (j * f[i][j][0][0]) % mod) % mod;
      f[i + 1][j + 1][0][1] =
          (f[i + 1][j + 1][0][1] % mod + f[i][j][0][0] % mod) % mod;
      f[i + 1][j + 1][1][0] =
          (f[i + 1][j + 1][1][0] % mod + f[i][j][0][0] % mod) % mod;
      f[i + 1][j][2][0] = (f[i + 1][j][2][0] % mod + f[i][j][0][1] % mod) % mod;
      f[i + 1][j][0][0] = (f[i + 1][j][0][0] % mod +
                           (max(i - j - 1, 0) * f[i][j][0][1]) % mod) %
                          mod;
      if (j >= 1)
        f[i + 1][j - 1][0][0] =
            (f[i + 1][j - 1][0][0] % mod + ((j - 1) * f[i][j][0][1]) % mod) %
            mod;
      f[i + 1][j + 1][0][1] =
          (f[i + 1][j + 1][0][1] % mod + f[i][j][0][1] % mod) % mod;
      f[i + 1][j][1][0] = (f[i + 1][j][1][0] % mod + f[i][j][0][1] % mod) % mod;
      f[i + 1][j][2][0] = (f[i + 1][j][2][0] % mod + f[i][j][1][0] % mod) % mod;
      f[i + 1][j][0][0] = (f[i + 1][j][0][0] % mod +
                           (max(i - j - 1, 0) * f[i][j][1][0]) % mod) %
                          mod;
      if (j >= 1)
        f[i + 1][j - 1][0][0] =
            (f[i + 1][j - 1][0][0] % mod + ((j - 1) * f[i][j][1][0]) % mod) %
            mod;
      f[i + 1][j][0][1] = (f[i + 1][j][0][1] % mod + f[i][j][1][0] % mod) % mod;
      f[i + 1][j + 1][1][0] =
          (f[i + 1][j + 1][1][0] % mod + f[i][j][1][0] % mod) % mod;
      f[i + 1][j][2][0] = (f[i + 1][j][2][0] % mod + f[i][j][1][1] % mod) % mod;
      f[i + 1][j][0][0] =
          (f[i + 1][j][0][0] % mod + (max(i - j, 0) * f[i][j][1][1]) % mod) %
          mod;
      if (j >= 1)
        f[i + 1][j - 1][0][0] =
            (f[i + 1][j - 1][0][0] % mod + ((j - 2) * f[i][j][1][1]) % mod) %
            mod;
      f[i + 1][j][0][1] = (f[i + 1][j][0][1] % mod + f[i][j][1][1] % mod) % mod;
      f[i + 1][j][1][0] = (f[i + 1][j][1][0] % mod + f[i][j][1][1] % mod) % mod;
      f[i + 1][j][2][0] = (f[i + 1][j][2][0] % mod + f[i][j][2][0] % mod) % mod;
      f[i + 1][j][0][0] = (f[i + 1][j][0][0] % mod +
                           (max(i - 1 - j, 0) * f[i][j][2][0]) % mod) %
                          mod;
      if (j >= 1)
        f[i + 1][j - 1][0][0] =
            (f[i + 1][j - 1][0][0] % mod + (j * f[i][j][2][0]) % mod) % mod;
      f[i + 1][j + 2][1][1] =
          (f[i + 1][j + 2][1][1] % mod + f[i][j][2][0] % mod) % mod;
    }
  }
  cout << (f[n][m][0][0] % mod + f[n][m][0][1] % mod + f[n][m][1][0] % mod +
           f[n][m][1][1] % mod + f[n][m][2][0] % mod) %
              mod
       << endl;
  return 0;
}
