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>
using namespace std;
#define ll long long
#define MOD 924844033
#define MAX 2020
void add(int &x,int y){x+=y;if(x>=MOD)x-=MOD;}
inline int read()
{
	int x=0;bool t=false;char ch=getchar();
	while((ch<'0'||ch>'9')&&ch!='-')ch=getchar();
	if(ch=='-')t=true,ch=getchar();
	while(ch<='9'&&ch>='0')x=x*10+ch-48,ch=getchar();
	return t?-x:x;
}
int g[MAX][MAX][4];
int f[MAX],jc[MAX];
int n,K,m,ans;
int main()
{
	n=read();K=read();m=(n-1)/K+1;
	jc[0]=1;
	for(int i=1;i<=n;++i)jc[i]=1ll*jc[i-1]*i%MOD;
	g[1][0][0]=1;g[1][1][2]=1;
	for(int i=1;i<m;++i)
		for(int j=0;j<=i;++j)
			for(int k=0;k<4;++k)
			{
				if(!g[i][j][k])continue;
				add(g[i+1][j][k>>1],g[i][j][k]);
				if(!(k&1))add(g[i+1][j+1][k>>1],g[i][j][k]);
				add(g[i+1][j+1][(k>>1)|2],g[i][j][k]);
			}
	f[0]=1;int s=0;
	for(int i=1;i<=K;++i)
	{
		int p=(n-i)/K+1;s+=p;
		for(int j=s;j;--j)
			for(int k=1;k<=p;++k)
				if(j>=k)add(f[j],1ll*f[j-k]*((g[p][k][0]+g[p][k][1])%MOD)%MOD);
	}
	for(int i=0;i<=n;++i)f[i]=1ll*f[i]*jc[n-i]%MOD;
	for(int i=0;i<=n;++i)add(ans,(i&1)?MOD-f[i]:f[i]);
	printf("%d\n",ans);
	return 0;
}