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;
#define N 2333
#define mod 924844033

int n,k,h[2*N],f[2*N][N],ans;

void pls(int &x,int y) {x=(x+y)%mod;}

int read(){
	int x=0,f=1;char ch=getchar();
	for (;!isdigit(ch);ch=getchar()) if (ch=='-') f=-f;
	for (;isdigit(ch);ch=getchar()) x=x*10+ch-'0';
	return x*f;
}

int main(){
	n=read();k=read();
	for (int i=1,t=0;i<=k;i++)
		h[t+=1+(n-i)/k]=1,h[t+=1+(n-i)/k]=1;
	f[0][0]=1;
	for (int i=0;i<=2*n;i++)
		for (int j=0;j<=n;j++){
			pls(f[i+1][j],f[i][j]);
			if (!h[i+1]) pls(f[i+2][j+1],f[i][j]);
		}
	for (int i=n,t=1;i>=0;i--,t=1ll*t*(n-i)%mod)
		ans=(ans+(i%2?-1ll:1ll)*f[2*n][i]*t)%mod;
	printf("%d\n",(ans+mod)%mod);return 0;
}