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>
#define mo 924844033
using namespace std;
int f[4010][2010],fac[2010],num[2010],st[4010],a[2010];
int main()
{
	int n,k;scanf("%d%d",&n,&k);
	fac[0]=1;
	for (int i=1;i<=n;i++) {fac[i]=(long long)fac[i-1]*i%mo;num[i%k]++;}
	for (int i=0;i<k;i++) a[num[i]]+=2;
	int js=0,top=0;
	for (int i=1;i<=n;i++)
	for (int j=1;j<=a[i];j++)
	{
		js++;
		for (int k=1;k<=i;k++) st[++top]=js;
	}
	f[0][0]=1;
	for (int i=1;i<=n*2;i++)
	{
		memcpy(f[i],f[i-1],n*4+10);
		if (st[i]==st[i-1]) for (int j=1;j<=n;j++) f[i][j]=(f[i][j]+f[i-2][j-1])%mo;
	}
	int ans=0;
	for (int i=0;i<=n;i++) ans=(ans+(long long)f[n*2][i]*fac[n-i]*((i&1)?-1:1))%mo;
	printf("%d\n",(ans+mo)%mo);
}