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<cmath>
#include<cstring>
#include<algorithm>
using namespace std;
const int N=4005,md=924844033;
int n,K,i,j,k,num,a[N],f[N][N][2],g[N][N],jc[N],ans;
int main()
{
	scanf("%d%d",&n,&K);
	for(i=1,num=0;i<=K;++i)
	{
		j=n/K+(i<=n%K?1:0);
		a[++num]=0;
		for(k=2;k<=j;++k)
			a[++num]=1;
		a[++num]=0;
		for(k=2;k<=j;++k)
			a[++num]=1;
	}
	jc[0]=1;
	for(i=1;i<=num;++i)
		jc[i]=1ll*jc[i-1]*i%md;
	f[1][0][0]=1;
	for(i=2;i<=num;++i)
		for(j=0;j<i;++j)
		{
			f[i][j][0]=(f[i-1][j][0]+f[i-1][j][1])%md;
			if(a[i]==1)
				f[i][j][1]=f[i-1][j-1][0];
		}
	for(i=0;i<=n;++i)
		ans=(ans+1ll*jc[n-i]*(f[num][i][0]+f[num][i][1])%md*(i&1?md-1:1)%md)%md;
	printf("%d",ans);
	return 0;
}