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>
const int MN=5000+5;
const int P=924844033;
using namespace std;
typedef long long ll;
template<typename T>inline T&IN(T&in){
	in=0;char c=getchar();int f=1;
	while(!isdigit(c)){if(c=='-')f=-1;c=getchar();}
	while(isdigit(c))in=in*10+c-'0',c=getchar();
	return in*=f;
}
int n,k;ll ans;
ll g[MN],fac[MN];
int eg[MN],f[MN][MN][2],vis[MN][2];
void input(){
	IN(n),IN(k);fac[0]=1;
	for(int i=1;i<=n;++i)for(int j=0;j<2;++j)if(!vis[i][j]){
		for(int x=i,y=j;x<=n;x+=k,y^=1)vis[x][y]=1,++eg[0];
		eg[eg[0]]=1;
	}
	f[1][0][0]=1;
	for(int i=1;i<=2*n;++i)for(int j=0;j<=n;++j){
		f[i+1][j][0]=(f[i][j][0]+f[i][j][1])%P;
		if(!eg[i])f[i+1][j+1][1]=f[i][j][0];
	}
	for(int i=0;i<=n;++i)g[i]=(f[2*n][i][0]+f[2*n][i][1])%P;
	for(int i=1;i<=n;++i)fac[i]=fac[i-1]*i%P;
	for(int i=0,j=-1;i<=n;++i,j=-j)ans=(ans+g[i]*j*fac[n-i]%P)%P;
	printf("%lld\n",(P-ans)%P);
}
int main(){
	input();
	return 0;
}