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<cstdio>
#include<algorithm>
#include<cstring>
#include<vector>
#include<queue>
using namespace std;
#define N 4005
#define INF 0x3f3f3f3f
#define MOD 924844033
int n,k;
bool vis[N][2],ed[N];
int tot;
int d[N][N][2],f[N],fac[N];
int rd()
{
	int f=1,x=0;char c=getchar();
	while(c<'0'||c>'9'){if(c=='-')f=-1; c=getchar();}
	while(c>='0'&&c<='9'){x=(x<<3)+(x<<1)+(c^48); c=getchar();}
	return f*x;
}
int main()
{
	n=rd(),k=rd();
	for(int i=1;i<=n;i++)
		for(int j=0;j<=1;j++)
			if(!vis[i][j])
			{
				int len=0;
				for(int x=i,y=j;x<=n;x+=k,y^=1)
				{
					vis[x][y]=1;
					len++;
				}
				tot+=len;
				ed[tot]=1;
			 }
	ed[0]=1;
	d[0][0][0]=1;
	for(int i=0;i<2*n;i++)
		for(int j=0;j<=n;j++)
		{
			d[i+1][j][0]=(d[i][j][0]+d[i][j][1])%MOD;
			if(!ed[i])
				d[i+1][j+1][1]=d[i][j][0];
		}
	for(int i=0;i<=n;i++)
		f[i]=(d[2*n][i][0]+d[2*n][i][1])%MOD;
	fac[0]=1;
    for(int i=1;i<=n;i++)
        fac[i]=1ll*fac[i-1]*i%MOD;
    int ans=0;
    for(int i=0,j=1;i<=n;i++,j=-j)
        ans=((1ll*ans+1ll*j*fac[n-i]*f[i]%MOD)%MOD+MOD)%MOD;
    printf("%d\n",ans);
	return 0;
}