Problem:
Score : 900 points

Problem Statement

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.

Sample Input 1

3 1

Sample Output 1

2

2 permutations (1, 2, 3), (3, 2, 1) satisfy the condition.

Sample Input 2

4 1

Sample Output 2

5

5 permutations (1, 2, 3, 4), (1, 4, 3, 2), (3, 2, 1, 4), (3, 4, 1, 2), (4, 2, 3, 1) satisfy the condition.

Sample Input 3

4 2

Sample Output 3

9

Sample Input 4

4 3

Sample Output 4

14

Sample Input 5

425 48

Sample Output 5

756765083

Solution in C++14 (Clang 3.8.0) (judge verdict: Accepted)

#include <cstdio>
const int Mod=924844033,N=2005;
int g[N<<1][N][2];bool end[N<<1];
int fac[N<<1];
inline int mo(int x){return x<Mod?x:x%Mod;}
int main (){
	int n,k;scanf ("%d%d",&n,&k);fac[0]=1;
	for (int i=1;i<=(n<<1);i++) fac[i]=1ll*fac[i-1]*i%Mod;
	for (int i=1,now=0;i<=k;i++){
		int d=(n-i)/k+1;
		end[now+=d]=true,end[now+=d]=true;
	}
	g[1][0][0]=1;
	for (int i=1;i<=(n<<1);i++)
		for (int j=0;j<=n;j++){
			g[i+1][j][0]=mo(g[i][j][0]+g[i][j][1]);
			if (!end[i]) g[i+1][j+1][1]=g[i][j][0];
		}
	int ans=0;
	for (int i=0;i<=n;i++){
		int now=1ll*fac[n-i]*(g[n+n][i][0]+g[n+n][i][1])%Mod;
		if (i&1) ans=mo(ans-now+Mod);
		else ans=mo(ans+now);
	}
	printf ("%d",ans);
	return 0;
}