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 <cstdio>

#define N 2001
#define M 924844033LL

long long f[2][N << 1][N], p[N], r;
int a[N << 1], n, k;

int main()
{
    scanf("%d%d", &n, &k);
    f[0][1][0] = 1;

    p[0] = p[1] = 1;
    for (int i = 2; i <= n; i++)
        p[i] = p[i - 1] * i % M;

    for (int i = 1; i <= k; i++)
    {
        for (int j = i; j <= n; j += k)
            a[++a[0]] = j;
        for (int j = i; j <= n; j += k)
            a[++a[0]] = j;
    }

    for (int i = 2; i <= n << 1; i++)
    {
        for (int j = 0; j <= i >> 1; j++)
        {
            f[0][i][j] = (f[0][i - 1][j] + f[1][i - 1][j]) % M;
            if (j && a[i] - a[i - 1] == k)
                f[1][i][j] = f[0][i - 1][j - 1];
        }
    }

    for (int i = 0; i <= n; i++)
    {
        long long g = (f[0][n << 1][i] + f[1][n << 1][i]) * p[n - i] % M;
        r = (r + ((i & 1) ? M - g : g)) % M;
    }

    printf("%lld\n", r);
    return 0;
}