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>
#include<queue>
using namespace std;
typedef long long lint;
#define mo 924844033
const int N=2333;
int n,m;
lint fac[N];
int ne[N<<1],ep,ni[N<<1];
lint dp[N<<1][N][2];
lint ans;
queue<int>q;
int main()
{
	scanf("%d%d",&n,&m);
	fac[0]=1;for(int i=1;i<=n;i++)fac[i]=fac[i-1]*i%mo;
	for(int i=1;i<=min(n,m);i++) q.push(i),q.push(i+n);
	int nw=q.front();q.pop();
	while(nw)
	{
		if((nw>n?nw-n:nw)+m<=n) ne[nw]=(nw>n?nw-n+m:nw+n+m),ni[nw]=1;
		else if(!q.empty()){ne[nw]=q.front();q.pop();}
		else ep=nw;
		nw=ne[nw];
	} 
	dp[1][0][0]=1;
	for(int i=1;ne[i];i=ne[i])
	{
		if(ni[i])
			for(int j=0;j<=n;j++)
			{
				(dp[ne[i]][j+1][1]+=dp[i][j][0])%=mo;
				(dp[ne[i]][j][0]+=dp[i][j][0]+dp[i][j][1])%=mo;
			}
		else for(int j=0;j<=n;j++) dp[ne[i]][j][0]=(dp[i][j][0]+dp[i][j][1])%mo;
	}
	for(int i=0;i<=n;i++)
		(ans+=((i&1)?-1ll:1ll)*((dp[ep][i][0]+dp[ep][i][1])%mo*fac[n-i]%mo)+mo)%=mo;
	printf("%lld\n",ans);
	return 0;
}