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<cstdio>
#include<algorithm>
using namespace std;
const int mod=924844033;
int n,k,tot,dp[4010][2010][2],fac[2010],vis[2010][2];
bool ck[4010];
void init(){
	fac[0]=1;
	for(int i=1;i<=n;i++)
		fac[i]=1ll*fac[i-1]*i%mod;
	return;
}
void DP(){
	for(int i=1;i<=n;i++)
		for(int j=0;j<2;j++)
			if(!vis[i][j]){
				for(int a=i,b=j;a<=n;a+=k,b^=1){
					vis[a][b]=1;
					++tot;
				}
				ck[tot]=1;
			}
	dp[1][0][0]=1;
	for(int i=1;i<=tot;i++)
		for(int j=0;j<=n;j++){
			dp[i+1][j][0]=dp[i][j][0]+dp[i][j][1];
			if(dp[i+1][j][0]>=mod)
				dp[i+1][j][0]-=mod;
			if(!ck[i])
				dp[i+1][j+1][1]=dp[i][j][0];
		}
	return;
}
int get_ans(){
	int ret=0;
	for(int i=0;i<=n;i++)
		ret=(ret+(i&1?mod-1ll:1ll)*fac[n-i]%mod*(dp[tot][i][0]+dp[tot][i][1]))%mod;
	return ret;
}
int main(){
	scanf("%d%d",&n,&k);
	init();
	DP();
	printf("%d",get_ans());
	return 0;
}