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 <cstring>
#define MOD 924844033
using namespace std;
const int MAXN = 2005;
int f[2][MAXN*2][MAXN],n,k,tot,g[MAXN],fac[MAXN];
bool ed[MAXN*2];
inline void add(int &x,int a)
{
	x+=a;
	if(x>=MOD)x-=MOD;
	if(x<0)x+=MOD;
}
int main()
{
	scanf("%d%d",&n,&k);
	for(int i=1;i<=k;++i){
		int len=0;
		int p=i,sta=1;
		while((sta==1 || p<=2*n) && (sta==-1 || p<=n)){
			++len;
			p+=k+sta*n;
			sta=-sta;
		}
		ed[tot+=len]=1;
	}
	for(int i=n+1;i<=n+k;++i){
		int len=0;
		int p=i,sta=-1;
		while((sta==1 || p<=2*n) && (sta==-1 || p<=n)){
			++len;
			p+=k+sta*n;
			sta=-sta;
		}
		ed[tot+=len]=1;
	}
	f[0][0][0]=1;
	ed[0]=1;
	for(int i=1;i<=n*2;++i)
		for(int j=0;j<=n;++j){
			f[0][i][j]=f[0][i-1][j]+f[1][i-1][j];
			if(f[0][i][j]>=MOD)f[0][i][j]-=MOD;
			if(!ed[i-1])f[1][i][j]=f[0][i-1][j-1];
		}
	fac[0]=1;
	for(int i=1;i<=n;++i)
		fac[i]=(long long)fac[i-1]*i%MOD;
	for(int i=0;i<=n;++i)
		g[i]=(long long)(f[0][n*2][i]+f[1][n*2][i])%MOD*fac[n-i]%MOD;
	int ans=0;
	for(int i=0,sta=1;i<=n;++i,sta=-sta)
		add(ans,g[i]*sta);
	cout<<ans<<endl;
	return 0;
}