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<cstring>
#include<algorithm>
#include<cmath>
#define inf 20021225
#define ll long long
#define mxn 2100
#define wph 924844033
using namespace std;

int f[mxn<<1][mxn<<1][2];
int n,fac[mxn<<1],k;
int a[mxn<<1],cnt; bool cant[mxn<<1];
int main()
{
	int ff,ans,tmp;
	scanf("%d%d",&n,&k);fac[0]=1;
	for(int i=1;i<=(n<<1);i++)	fac[i] = (ll)fac[i-1]*i%wph;
	for(int i=1;i<=k;i++)
	for(int j=0;j<=1;j++)
	for(int l=i;l<=n;l+=k)
	{
		++cnt;
		if(l==i)	cant[cnt]=1;
	}
	f[0][0][0]=1;
	for(int i=1;i<=cnt;i++)
	for(int j=0;j<=i;j++)
	{
		f[i][j][0]=(f[i-1][j][0]+f[i-1][j][1])%wph;
		if(!cant[i])	f[i][j][1]=f[i-1][j-1][0];
	}
	ans=0;
	for(int i=0;i<=n;i++)
	{
		ff=i&1?-1:1;
		tmp=((ll)f[cnt][i][0]+f[cnt][i][1])%wph*fac[n-i]%wph;
		ans=((ll)ans+ff*tmp+wph)%wph;
	}
	printf("%d\n",ans);
	return 0;
}