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 maxn 4005
#define mod 924844033
int n,k,tot,dp[maxn][maxn][2],f[maxn],fact[maxn],ans;
bool vis[maxn][2],ed[maxn];
int main()
{
	scanf("%d%d",&n,&k);
	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]=true; dp[0][0][0]=1;
	for(int i=0;i<2*n;i++)
		for(int j=0;j<=n;j++)
		{
			dp[i+1][j][0]=(dp[i][j][0]+dp[i][j][1])%mod;
			if(!ed[i]) dp[i+1][j+1][1]=dp[i][j][0];
		}
	for(int i=0;i<=n;i++) f[i]=(dp[n*2][i][0]+dp[n*2][i][1])%mod;
	fact[0]=1;
	for(int i=1;i<=n;i++) fact[i]=1ll*fact[i-1]*i%mod;
	for(int i=0,j=1;i<=n;i++,j=-j) ans=(ans+1ll*j*f[i]*fact[n-i]%mod)%mod;
	printf("%d\n",(ans+mod)%mod);
}