Problem: Snuke loves permutations. He is making a permutation of length N.

Since he hates the integer K, his permutation will satisfy the following:

* Let the permutation be a_1, a_2, ..., a_N. For each i = 1,2,...,N, |a_i - i| \neq K.



Among the N! permutations of length N, how many satisfies this condition?

Since the answer may be extremely large, find the answer modulo 924844033(prime).

Constraints

* 2 ≦ N ≦ 2000
* 1 ≦ K ≦ N-1

Input

The input is given from Standard Input in the following format:


N K


Output

Print the answer modulo 924844033.

Examples

Input

3 1


Output

2


Input

4 1


Output

5


Input

4 2


Output

9


Input

4 3


Output

14


Input

425 48


Output

756765083

Solution (in CPP):

Solution:
#include<bits/stdc++.h>

using namespace std;

const int Mod = 924844033;
const int N = 5e3 + 10;

int n, k, mark[N], g[N][N][2];
int fac[N], tot = 0;

int add(int a, int b) {
  return (a += b) >= Mod ? a - Mod : a;
}

int sub(int a, int b) {
  return (a -= b) < 0 ? a + Mod : a;
}

int mul(int a, int b) {
  return 1ll * a * b % Mod;
}

int main() {
  scanf("%d %d", &n, &k);
  fac[0] = 1;
  for (int i = 1; i <= n; i++) {
    fac[i] = mul(fac[i - 1], i);
  }
  for (int i = 1; i <= k; i++) {
    for (int j = i; j <= n; j += k) {
      mark[++tot] = (j != i);
    }
    for (int j = i; j <= n; j += k) {
      mark[++tot] = (j != i);
    }
  }
  g[0][0][0] = 1;
  for (int i = 1; i <= 2 * n; i++) {
    for (int j = 0; j <= i; j++) {
      g[i][j][0] = add(g[i - 1][j][1], g[i - 1][j][0]);
      if (mark[i]) g[i][j][1] = g[i - 1][j - 1][0];
    }
  }
  int ans = 0;
  for (int i = 0; i <= n; i++) {
    if (i & 1) {
      ans = sub(ans, mul(fac[n - i], add(g[2 * n][i][0], g[2 * n][i][1])));
    } else {
      ans = add(ans, mul(fac[n - i], add(g[2 * n][i][0], g[2 * n][i][1])));
    }
  }
  printf("%d\n", ans);
  return 0;
}