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>
#define N 2002
#define p 924844033
inline int mod(int x){return x<p?x:x-p;}
int a[N],f[N][2],i,j,m,n,s,x;
int main()
{
	scanf("%d%d",&n,&m),f[0][0]=1;
	for(i=1;i<=m;i++)
	{
		for(j=0;j<=n;f[j++][0]=0)f[j][1]=mod(f[j][0]+f[j][1]);
		for(s=(n-i)/m+2>>1;s--;)
		for(j=n;j--;)
		{
			f[j+1][0]=mod(f[j+1][0]+f[j][0]);
			f[j+1][1]=mod(f[j+1][1]+mod(f[j][0]+f[j][1]));
			f[j][0]=mod(f[j][0]+f[j][1]);
			f[j][1]=0;
		}
		if(~((n-i)/m)&1)for(j=0;j<=n;j++)f[j][1]=0;
	}
	for(;i<=n&&i<=m<<1;i++)
	{
		for(j=0;j<=n;f[j++][1]=0)f[j][0]=mod(f[j][0]+f[j][1]);
		for(s=(n-i)/m+2>>1;s--;)
		for(j=n;j--;)
		{
			f[j+1][0]=mod(f[j+1][0]+f[j][0]);
			f[j+1][1]=mod(f[j+1][1]+mod(f[j][0]+f[j][1]));
			f[j][0]=mod(f[j][0]+f[j][1]);
			f[j][1]=0;
		}
		if(~((n-i)/m)&1)for(j=0;j<=n;j++)f[j][1]=0;
	}
	for(i=*a=1;i<=n;i++)a[i]=(long long)a[i-1]*i%p;
	for(i=0;i<=n;i++)x=i&1?(x+(long long)(p-a[n-i])*(f[i][0]+f[i][1]))%p:(x+(long long)a[n-i]*(f[i][0]+f[i][1]))%p;
	return 0&printf("%d\n",x);
}