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>
#include<cstdlib>
#define N 4010
#define ll long long
#define mod 924844033
using namespace std;
ll fac[N];
ll f[N][N],g[N][N];
int link[N];
int main()
{
	int n,m;
	scanf("%d%d",&n,&m);
	fac[0]=1;
	for(int i=1;i<=n<<1;i++) fac[i]=fac[i-1]*i%mod;
	int tot=0;
	for(int i=1;i<=m;i++)
	{
		for(int j=i;j<=n;j+=m)
		{
			tot++;
			if(j!=i) link[tot]=1;
		}
		for(int j=i;j<=n;j+=m)
		{
			tot++;
			if(j!=i) link[tot]=1;
		}
	}
	f[0][0]=1;
	for(int i=0;i<n*2;i++)
		for(int j=0;j<=n;j++)
		{
			f[i+1][j]=(f[i][j]+g[i][j])%mod;
			if(link[i+1]) g[i+1][j+1]=f[i][j];
		}
	ll ans=0;
	for(int i=0;i<=n;i++)
	ans=(ans+(f[2*n][i]+g[2*n][i])*fac[n-i]*(i&1?-1:1)+mod)%mod;
	printf("%lld",ans);
	return 0;
}