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 ll long long
#define pi acos(-1)
#define inf 2e9 
using namespace std;
const int mod=924844033;
const int N=4005;
inline ll rd(){
	ll x=0,f=1;char ch=getchar();
	while(ch<'0'||ch>'9'){if(ch=='-') f=0;ch=getchar();}
	while(ch>='0'&&ch<='9'){x=(x<<3)+(x<<1)+(ch^48);ch=getchar();}
	return f?x:-x;
}int n,m,tot;bool vis[N];
ll f[N][N][2],fac[N],ans;
int main(){
	n=rd(),m=rd();fac[0]=1; 
	for(int i=1;i<=n;i++) fac[i]=fac[i-1]*i%mod;
	for(int i=1;i<=m;i++){
		for(int t=2;t--;){
			for(int j=i;j<=n;j+=m){
				tot++;if(j!=i) vis[tot]=1;
			}
		}
	}f[0][0][0]=1;
	for(int i=0;i<n*2;i++){
		for(int j=0;j<=n;j++){
			f[i+1][j][0]=(f[i][j][0]+f[i][j][1])%mod;
			if(vis[i+1]) f[i+1][j+1][1]=f[i][j][0];
		}
	} 
	for(int i=0,t=1;i<=n;i++,t=-t){
		f[2*n][i][0]=1ll*(f[2*n][i][0]+f[2*n][i][1])*fac[n-i]%mod;
		ans=(ans+f[2*n][i][0]*t+mod)%mod; 
	}cout<<ans;
	return 0;
}