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>
#include <algorithm>
#include <cstring>
#include <cctype>
using namespace std;
inline int read(int f = 1, int x = 0, char ch = ' ')
{
    while(!isdigit(ch = getchar())) if(ch == '-') f = -1;
    while(isdigit(ch)) x = x*10+ch-'0', ch = getchar();
    return f*x;
}
const int N = 4e3+5, P = 924844033;
int n, m;
int cut[N], h[N][N][2], g[N], f[N], fac[N];
int main()
{
    n = read(), m = read(); fac[0] = 1;
    for(int i = 1; i <= n; ++i) fac[i] = 1ll*fac[i-1]*i%P;
    for(int i = 1, p = 1; i <= m; ++i)
    {
        cut[p] = 1; p += (n-i)/m+1;
        cut[p] = 1; p += (n-i)/m+1;
    }
    for(int i = 0; i <= n<<1; ++i) h[i][0][0] = 1;
    for(int i = 1; i <= n<<1; ++i)
        for(int j = 1; j <= n; ++j)
        {
            h[i][j][0] = (h[i-1][j][0]+h[i-1][j][1])%P;
            if(!cut[i]) h[i][j][1] = h[i-1][j-1][0];
        }
    for(int i = 0; i <= n; ++i) g[i] = 1ll*(h[n<<1][i][0]+h[n<<1][i][1])*fac[n-i]%P;
    for(int i = 0, w = 1; i <= n; ++i, w = P-w) f[n] = (f[n]+1ll*w*g[i]%P)%P; 
    printf("%d\n", f[n]);
    return 0;
}