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 ll long long
using namespace std;
const int mod=924844033;
ll f[4010][2010][2],fac[2010];
int nxt[5010],e[5010],pre[5010];
int read()
{
	int x=0;char c=getchar(),flag='+';
	while(!isdigit(c)) flag=c,c=getchar();
	while(isdigit(c)) x=x*10+c-'0',c=getchar();
	return flag=='-'?-x:x;
}
int main()
{
	int n=read(),k=read(),cnt=0;
	for(int i=1;i<=n;i++) 
	{
		if(i+k<=n) nxt[i]=i+k+n,pre[i+k+n]=i;
		if(i-k>=1) nxt[i-k+n]=i,pre[i]=i-k+n;
	}
	for(int i=1;i<=2*n;i++)
	{
		if(!pre[i])
		{
			int x=i;
			cnt++;
			while(nxt[x]) x=nxt[x],e[++cnt]=1;
		}
	}
//	cout<<cnt;
//for(int i=1;i<=cnt;i++) cout<<e[i]<<' ';
	f[0][0][0]=1;
	for(int i=1;i<=cnt;i++)
	{
		for(int j=0;j<=n;j++)
		{
			f[i][j][0]=(f[i-1][j][0]+f[i-1][j][1])%mod;
			if(e[i]&&j) f[i][j][1]=f[i-1][j-1][0];
		}
	}
	ll ans=1;
	for(int i=1;i<=n;i++) ans=ans*i%mod;
	fac[0]=1;
	for(int i=1;i<=n;i++) fac[i]=fac[i-1]*i%mod;
	for(int i=1;i<=n;i++)
	{
		if(i&1) ans=(ans-(f[cnt][i][0]+f[cnt][i][1])*fac[n-i]%mod+mod)%mod;
		else ans=(ans+(f[cnt][i][0]+f[cnt][i][1])*fac[n-i])%mod;
	}
	cout<<ans;
	return 0;
}