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<iostream>
#include<cstdio>
#define N (4009)
#define MOD (924844033)
using namespace std;

long long n,k,vis[N],tot,g[N],f[N][N][2],fac[N];

int main()
{
	scanf("%lld%lld",&n,&k);
	for (int t=1; t<=2; ++t)
		for (int i=1; i<=k; ++i)
			for (int j=i; j<=n; j+=k)
			{
				tot++;
				if (j!=i) vis[tot]=true; 
			}
	f[0][0][0]=1;
	for (int i=1; i<=2*n; ++i)
		for (int j=0; j<=n; ++j)
		{
			(f[i][j][0]+=f[i-1][j][0]+f[i-1][j][1])%=MOD;
			if (vis[i]) (f[i][j][1]+=f[i-1][j-1][0])%=MOD;
		}
	for (int i=0; i<=n; ++i)
		g[i]=(f[2*n][i][0]+f[2*n][i][1])%MOD;
	
	fac[0]=1;
	for (int i=1; i<=n; ++i) fac[i]=fac[i-1]*i%MOD;
	long long ans=fac[N];
	for (int i=0,j=-1; i<=n; ++i,j=-j)
		(ans-=j*g[i]*fac[n-i]%MOD)%=MOD;
	printf("%lld\n",(ans+MOD)%MOD);
}