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 <algorithm>
#include <cstdio>
#include <cstring>
#include <cctype>
#define int long long 
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, k;
int ille[N], t;
int f[N][N][2], fac[N];
int ans;
signed main()
{
    n = read(), k = read(); fac[0] = 1;
    for(int i = 1; i <= n; ++i) fac[i] = 1ll*fac[i-1]*i%P;
    for(int i = 1; i <= k; ++i)
    {
        int j = (n-i)/k+1;
        t += j; ille[t] = true;
        t += j; ille[t] = true;
    }
    f[1][0][0] = 1;
    for(int i = 1; i <= n<<1; ++i)
        for(int j = 0; j <= n; ++j)
        {
            f[i+1][j][0] = (f[i][j][0]+f[i][j][1])%P;
            if(!ille[i]) f[i+1][j+1][1] = f[i][j][0];
        }
    for(int i = 0; i <= n; ++i)
    {
        int g = 1ll*(f[n<<1][i][0]+f[n<<1][i][1])%P*fac[n-i]%P;
        if(i&1) ans = ((ans-g)%P+P)%P;
        else ans = (ans+g)%P;
    }
    printf("%lld\n", ans);
    return 0;
}