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 <iostream>
#include <algorithm>
typedef long long ll;
using namespace std;

ll mod=924844033, dp[2010][2010][2]={}, ep[4010][2010]={}, frac[2010];

int main(void){
    int N, K;
    cin >> N >> K;
    dp[0][0][0]=dp[0][0][1]=1;
    for(int i=0; i<=2000; ++i){
        for(int j=0; j<=i; ++j){
            (dp[i+1][j][0] += dp[i][j][0]) %= mod;
            (dp[i+1][j][1] += dp[i][j][0]) %= mod;
            (dp[i+1][j+1][0] += dp[i][j][1]) %= mod;
        }
    }
    ep[0][0]=1;
    for(int i=0; i<K*2; ++i){
        int num=(N-i/2-1)/K;
        for(int j=0; j+(num+1)/2<=N; ++j){
            for(int k=0; k<=(num+1)/2; ++k){
                (ep[i+1][j+k] += (ep[i][j]*dp[num][k][0])%mod) %= mod;
            }
        }
    }
    frac[0]=1;
    for(int i=1; i<=N; ++i) frac[i]=(frac[i-1]*i)%mod;
    ll ans=frac[N];
    for(int i=1; i<=N; ++i){
        if(i%2==1){
            (ans += mod-(frac[N-i]*ep[K*2][i])%mod) %= mod;
        }
        else{
            (ans += (frac[N-i]*ep[K*2][i])%mod) %= mod;
        }
    }
    cout << ans << endl;
    return 0;
}