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>
const int mod=924844033;
long long dp[4010][2010][2],g[4010],f[4010];
bool vis[2010][2],End[4010];
int n,K;
int ADD(int x)
{
	return (x>=mod)?x-mod:x;
}
int main()
{
	scanf("%d%d",&n,&K);
	int sum=0;
	for (int i=1;i<=n;i++)
		for (int j=0;j<=1;j++)
		{
			if (vis[i][j]) continue;
			int len=0;
			for (int x=i,y=j;x<=n;x+=K,y^=1)
			{
				vis[x][y]=true;
				len++;
			}
			sum+=len;
			End[sum]=true;
		}
	dp[0][0][0]=1;
	for (int i=1;i<=(n<<1);i++)
		for (int j=0;j<=n;j++)
		{
			dp[i][j][0]=ADD(dp[i-1][j][0]+dp[i-1][j][1]);
			if (j>0&&!End[i]) dp[i][j][1]=dp[i-1][j-1][0];
		}
	f[0]=1;
	for (int i=1;i<=n;i++) f[i]=f[i-1]*i%mod;
	for (int i=0;i<=n;i++) g[i]=ADD(dp[(n<<1)][i][0]+dp[(n<<1)][i][1]);
	int j=1;
	long long ans=0;
	for (int i=0;i<=n;i++)
		ans=(ans+g[i]*f[n-i]%mod*j%mod+mod)%mod,j=-j;
	printf("%lld\n",ans);
	return 0;
}