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;
template <class T>
void read(T &x) {
  x = 0;
  char c = getchar();
  long long f = 0;
  while (c < '0' || c > '9') f |= (c == '-'), c = getchar();
  while (c >= '0' && c <= '9')
    x = (x << 3) + (x << 1) + (c ^ 48), c = getchar();
  if (f) x = -x;
}
template <class T>
bool checkmax(T &a, T b) {
  return b > a ? a = b, 1 : 0;
}
template <class T>
bool checkmin(T &a, T b) {
  return b < a ? a = b, 1 : 0;
}
const long long mod = 1e9 + 7;
template <class T>
void my_add(T &a, T b) {
  b %= mod;
  a = a + b > mod ? a + b - mod : a + b;
}
template <class T>
void my_sub(T &a, T b) {
  b %= mod;
  a = a - b < 0 ? a - b + mod : a - b;
}
namespace moonpie {
const long long N = 1005;
long long n, m, dp[N][N][2][2], F[N], G[N], pi[N], inv[N];
long long qpow(long long x, long long y) {
  long long res = 1;
  for (long long i = 0; (1 << i) <= y; ++i, x = x * x % mod)
    if (y & (1 << i)) res = res * x % mod;
  return res;
}
long long C(long long n, long long m) {
  if (m > n || m < 0) return 0;
  if (m == n || m == 0) return 1;
  return pi[n] * inv[m] % mod * inv[n - m] % mod;
}
void solve() {
  pi[0] = 1;
  for (long long i = 1; i < N; ++i) pi[i] = pi[i - 1] * i % mod;
  inv[N - 1] = qpow(pi[N - 1], mod - 2);
  for (long long i = N - 2; i >= 0; --i) inv[i] = inv[i + 1] * (i + 1) % mod;
  cin >> n >> m;
  dp[1][0][0][0] = dp[1][1][0][1] = 1;
  for (long long i = 2; i < n; ++i) {
    dp[i][0][0][0] = 1;
    for (long long j = 1; j <= i; ++j) {
      my_add(dp[i][j][0][0], dp[i - 1][j - 1][0][0]);
      my_add(dp[i][j][1][0], dp[i - 1][j - 1][0][1]);
      my_add(dp[i][j][0][1], dp[i - 1][j - 1][0][0] + dp[i - 1][j - 1][1][0]);
      my_add(dp[i][j][1][1], dp[i - 1][j - 1][0][1] + dp[i - 1][j - 1][1][1]);
      my_add(dp[i][j][0][0], dp[i - 1][j][1][0] + dp[i - 1][j][0][0]);
      my_add(dp[i][j][1][0], dp[i - 1][j][0][1] + dp[i - 1][j][1][1]);
    }
  }
  dp[n][0][0][0] = 1;
  for (long long j = 1; j <= n; ++j) {
    my_add(dp[n][j][0][0], dp[n - 1][j - 1][0][0]);
    my_add(dp[n][j][1][0], dp[n - 1][j - 1][0][1]);
    my_add(dp[n][j][0][0], dp[n - 1][j][1][0] + dp[n - 1][j][0][0]);
    my_add(dp[n][j][1][0], dp[n - 1][j][0][1] + dp[n - 1][j][1][1]);
  }
  for (long long i = 0; i <= n; ++i) {
    F[i] = (dp[n][i][1][0] + dp[n][i][0][0]) * pi[n - i] % mod;
  }
  long long ans = 0;
  for (long long i = m; i <= n; ++i) {
    if ((i - m) & 1)
      my_sub(ans, F[i] * C(i, m));
    else
      my_add(ans, F[i] * C(i, m));
  }
  cout << ans << endl;
}
}  // namespace moonpie
signed main() {
  moonpie::solve();
  return 0;
}
