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<ctime>
#include<iostream>
using namespace std;
const int md=924844033;
long long dp[2010];
int a[2010];
bool vis[2010];
int f[2010][2010][2];
long long fac[2010];
int n,k;
int main(){
//	freopen("c.in","r",stdin);
//	freopen("c.out","w",stdout);
	scanf("%d%d",&n,&k);
	fac[0]=1;
	for(int i=1;i<=2000;i++)
		fac[i]=fac[i-1]*i%md;
	int p,cnt1,cnt2;
	f[1][0][0]=1;
	f[1][1][1]=1;
	for(int i=2;i<=2000;i++)
	{
		for(int j=0;j<=i;j++)
		{
			if(j>0)
				f[i][j][1]=f[i-1][j-1][0]%md;
			f[i][j][0]=(f[i-1][j][1]+f[i-1][j][0])%md;
		}
	}
	dp[0]=1;
	for(int i=1;i<=n;i++){
		if(!vis[i]){
			cnt1=cnt2=0;
			p=i;
			vis[p]=1;
			if(i-k>0) cnt1++;
			while(p+2*k<=n){
				cnt1++,cnt2++;
				p=p+k*2;
				vis[p]=1;
			}
			if(p+k<=n) cnt2++;
			cnt1=cnt1+cnt2;
			for(int j=0;j<=cnt1;j++)
				a[j]=(f[cnt1][j][1]+f[cnt1][j][0])%md;
			for(int j=n;j>=0;j--)
				for(int s=1;s<=cnt1&&s<=j;s++)
					dp[j]=(dp[j]+dp[j-s]*a[s])%md;
		}
	}
	long long ans=0;
	for(int i=0;i<=n;i++)
		ans=(ans+fac[n-i]*dp[i]%md*((i&1)?-1:1)+md)%md;
	printf("%lld\n",ans);
	return 0;
}