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 N 2005
using namespace std;
const int mod=924844033;
int n,k;
long long dp[2][N][2];
int st[N*2],f[N],fac[N];//start point
int main(){
	scanf("%d%d",&n,&k);
	int len=1;st[1]=1;
	for(int i=1;i<=k;i++){
		int d=(n-i)/k+1;
		len+=d;st[len]=1;
		len+=d;st[len]=1;
	}
	int now=0;
	dp[now][0][0]=1;
	for(int i=1;i<len;i++){
		memset(dp[now^1],0,sizeof(dp[0]));
		for(int j=0;j<min(i,n+1);j++){
			dp[now^1][j][0]+=dp[now][j][0]+dp[now][j][1];//不选
			if(st[i+1]!=1) dp[now^1][j+1][1]+=dp[now][j][0];
			dp[now^1][j][0]%=mod;
			dp[now^1][j][1]%=mod;
		}
		now^=1;
	}
	for(int i=0;i<=n;i++) f[i]=(dp[now][i][0]+dp[now][i][1])%mod;
	long long ans=0;
	fac[0]=1;
	for(int i=1;i<=n;i++) fac[i]=fac[i-1]*1LL*i%mod;
	for(int i=0,j=1;i<=n;i++,j=-j)
		ans=(ans+f[i]*1LL*fac[n-i]*j)%mod;
	cout<<(ans+mod)%mod<<endl;
	return 0;
}