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>
using namespace std;
const int maxn=2003;
const int mod=924844033;
int n,K,m,Rem;
unsigned f[maxn][maxn][3],g[maxn];
int dp[maxn],Fac[maxn];
int main(){
	scanf("%d%d",&n,&K);
	m=n/(2*K)+1,Rem=n%(2*K);
	Fac[0]=1;
	for(int i=1;i<=n;i++)Fac[i]=Fac[i-1]*1ll*i%mod;
	dp[0]=1;
	int cnt=0;
	for(int i=1;i<=2*K;i++){
		int Lim=m-(Rem<i),Bot=i,Top=(Lim-1)*2*K+i;
		f[0][0][2]=1;
		for(int j=1;j<=Lim;j++){
			for(int k=0;k<=j;k++){
				f[j][k][0]=f[j][k][1]=0;
				if(j<Lim||Top+K<=n)f[j][k][0]=(f[j-1][k-1][0]+f[j-1][k-1][1]+f[j-1][k-1][2])%mod;
				if(j>1||Bot-K>=1)f[j][k][1]=(f[j-1][k-1][1]+f[j-1][k-1][2])%mod;
				f[j][k][2]=(f[j-1][k][0]+f[j-1][k][1]+f[j-1][k][2])%mod;
			}
		}
		for(int j=1;j<=Lim;j++)g[j]=(f[Lim][j][0]+f[Lim][j][1]+f[Lim][j][2])%mod;
		cnt+=Lim;
		for(int j=n;j>=0;j--){
			for(int k=1;k<=Lim&&k<=j;k++){
				dp[j]=(dp[j]+dp[j-k]*1ll*g[k])%mod;
			}
		}
	}
	int Ans=0;
	for(int i=0;i<=n;i++){
		Ans=(Ans+((i&1)?(mod-1ll):(1ll))*dp[i]%mod*Fac[n-i])%mod;
	}
	printf("%d\n",Ans);
	return 0;
}