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>

const int mod=924844033;

const int N=2005;

int n,k,vis[N],a[N],a_cnt,fac[N],ans;

long long f[N][N][2][2];

int main(){
	scanf("%d%d",&n,&k); a[0]=a[n+1]=1e9;
	for(int i=1;i<=n;++i) if(!vis[i]) for(int j=i;j<=n;j+=k) vis[j]=1,a[++a_cnt]=j;
	for(int i=0;i<=n;++i){
		f[i][0][0][0]=1;
		for(int j=1;j<=i;++j){
			f[i][j][0][0]=(f[i-1][j][0][0]+f[i-1][j][1][0]+(a[i]-a[i-1]==k)*f[i-1][j-1][0][0])%mod;
			f[i][j][0][1]=(a[i+1]-a[i]==k)*(f[i-1][j-1][0][0]+f[i-1][j-1][1][0])%mod;
			f[i][j][1][0]=(f[i-1][j][0][1]+f[i-1][j][1][1]+(a[i]-a[i-1]==k)*f[i-1][j-1][0][1])%mod;
			f[i][j][1][1]=(a[i+1]-a[i]==k)*(f[i-1][j-1][0][1]+f[i-1][j-1][1][1])%mod;
		}
	}
	fac[0]=1; for(int i=1;i<=n;++i) fac[i]=1ll*fac[i-1]*i%mod;
	for(int i=0,t=1;i<=n;++i,t=mod-t){
		int res=0;
		for(int p=0;p<2;++p) for(int q=0;q<2;++q) res=(res+f[n][i][p][q])%mod;
		ans=(ans+1ll*t*res%mod*fac[n-i]%mod)%mod;
	}
	printf("%d\n",ans);
	return 0;
}