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>
#define rep(i,x,y) for (int i=(x);i<=(y);i++)
#define ll long long
using namespace std;
const int N=4100,mod=924844033;
int n,m,K,b[N],f[N][N][2],vis[N],g[N],ans,fac[N];
int main(){
	scanf("%d%d",&n,&K); fac[0]=1;
	rep (i,1,n){
		if (!vis[i]){
			for (int j=i;j<=n;j+=K) ++m;
			b[m]=1;
			for (int j=i;j<=n;j+=K) ++m,vis[j]=1;
			b[m]=1;
		}
		fac[i]=(ll)fac[i-1]*i%mod;
	}
	f[1][0][0]=1;
	rep (i,2,m)
		rep (j,0,n){
			f[i][j][0]=(f[i-1][j][0]+f[i-1][j][1])%mod;
			if (!b[i-1]&&j) f[i][j][1]=f[i-1][j-1][0];
		}
	for (int i=0,op=1;i<=n;i++,op=-op){
		g[i]=(f[m][i][0]+f[m][i][1])%mod;
		ans=(ans+(ll)g[i]*fac[n-i]%mod*op+mod)%mod;
	}
	printf("%d\n",ans);
	return 0;
}