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;
const int mxn=5010,md=924844033;
int n,k,a[mxn],fct[mxn],f[mxn][2],g[mxn][2];
int main()
{
	cin >> n >> k;
	fct[0]=1;
	for (int i=1;i<=n;++i)
		fct[i]=1ll*fct[i-1]*i%md;
	f[0][0]=1;
	for (int i=1;i<=n&&i<=k;++i){
		int m=(n-i)/k;
		for (int j=1;j<=m;++j)
			for (int l=n;l>=0;--l){
				f[l][0]=(f[l][0]+f[l][1])%md;
				if (l) f[l][1]=f[l-1][0];
			}
		for (int j=0;j<=n;++j)
			f[j][0]=(f[j][0]+f[j][1])%md,f[j][1]=0;
		for (int j=1;j<=m;++j)
			for (int l=n;l>=0;--l){
				f[l][0]=(f[l][0]+f[l][1])%md;
				if (l) f[l][1]=f[l-1][0];
			}
		for (int j=0;j<=n;++j)
			f[j][0]=(f[j][0]+f[j][1])%md,f[j][1]=0;
	}
	int ans=0;
	for (int i=0,flg=1;i<=n;++i,flg*=-1)
		ans=(ans+1ll*flg*f[i][0]*fct[n-i])%md;
	cout << (ans+md) % md << '\n';
	return 0;
}