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 LL long long
#define Mod 924844033
#define MN 2005
int n,k,id[MN<<1],tot;
LL fac[MN],f[MN<<1][MN][2];
int main(){
	scanf("%d%d",&n,&k);
	fac[0]=1;
	for(int i=1;i<=n;++i)fac[i]=(LL)fac[i-1]*i%Mod;
	for(int i=1;i<=k;++i){
		for(int j=i;j<=n;j+=k)
			id[++tot]=j;
		for(int j=i;j<=n;j+=k)
			id[++tot]=j;
	}
	f[1][0][0]=1;
	for(int i=2;i<=(n<<1);++i)
		for(int j=0;j<=i/2;++j){
			f[i][j][0]=(f[i-1][j][0]+f[i-1][j][1])%Mod;
			if(j&&id[i]-id[i-1]==k)
				f[i][j][1]=f[i-1][j-1][0];
		}
	LL ans=fac[n];
	for(int i=1;i<=n;++i)
		ans=(ans+((i&1)?-1ll:1ll)*(LL)(f[n<<1][i][0]+f[n<<1][i][1])*(LL)fac[n-i]%Mod+Mod)%Mod;
	printf("%lld",ans);
	return 0;
}