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 N=1e6+5;
const int P=924844033;
int n,d,len=1,f[N][2],g[N][2];
long long fac[N];
int main(){
	scanf("%d%d",&n,&d),fac[0]=fac[1]=f[0][0]=g[0][0]=1;
	for(int i=2;i<=n;i++)	fac[i]=fac[i-1]*i%P;
	for(int i=1;i<=d;i++){
		for(int j=1;j<=len;j++)
			g[j][0]=(g[j][0]+g[j][1])%P,g[j][1]=0;
		for(int j=i+d;j<=n;j+=d,++len){
			for(int k=1;k<=len;k++){
				f[k][0]=(g[k][0]+g[k][1])%P;
				f[k][1]=g[k-1][0];
			}
			for(int k=1;k<=len;k++){
				g[k][0]=f[k][0];
				g[k][1]=f[k][1];
			}
		}
	}
	for(int i=d+1;i<=d*2;i++){
		for(int j=1;j<=len;j++)
			g[j][0]=(g[j][0]+g[j][1])%P,g[j][1]=0;
		for(int j=i;j<=n;j+=d,++len){
			for(int k=1;k<=len;k++){
				f[k][0]=(g[k][0]+g[k][1])%P;
				f[k][1]=g[k-1][0];
			}
			for(int k=1;k<=len;k++){
				g[k][0]=f[k][0];
				g[k][1]=f[k][1];
			}
		}
	}
	long long ans=fac[n];
	for(int i=1;i<=n;i++)
		ans=(ans+(i&1?-1:1)*fac[n-i]*(f[i][0]+f[i][1])%P)%P;
	printf("%lld\n",(ans+P)%P);
	return 0;
}