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=4040,p=924844033;
int fac[maxn],dp[maxn][maxn][2],a[maxn],g[maxn],n,k,tot;
int main(){
	cin>>n>>k;
	fac[0]=1;for(int i=1;i<=n;++i)fac[i]=1ll*fac[i-1]*i%p;
	for(int i=1;i<=k;++i){
		for(int j=i;j<=n;j+=k)a[++tot]=j;
        for(int j=i;j<=n;j+=k)a[++tot]=j;
	}
	dp[1][0][0]=1;
	for(int i=2;i<=tot;++i)
		for(int j=0;j<=min(n,i/2);++j){
			dp[i][j][0]=(dp[i-1][j][1]+dp[i-1][j][0])%p;
			if(j>0&&a[i]-a[i-1]==k)dp[i][j][1]=dp[i-1][j-1][0];
		}
	for(int i=0;i<=n;++i)g[i]=1ll*(dp[tot][i][0]+dp[tot][i][1])*fac[n-i]%p;
	int ans=0;
	for(int i=0;i<=n;++i){
		if(i&1)ans=(ans+p-g[i])%p;else ans=(ans+g[i])%p;
	}
	cout<<ans;
}