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 (GCC 5.4.1) (judge verdict: Accepted)

#include<bits/stdc++.h>
using namespace std;
typedef long long LL;
const int maxn=2010,maxm=maxn<<1;
#define mod 924844033
int vis[maxn][2],ed[maxm];
int tot;LL f[maxm][maxn][2],fac[maxn];
int main(){
	int n,k;
	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++;
				}
				ed[tot+=len]=1;
			}
		}
	}
	f[1][0][0]=1;
	for(int i=1;i<tot;++i){
		for(int j=0;j<=n;++j){
			f[i+1][j][0]=(f[i][j][1]+f[i][j][0])%mod;
			if(!ed[i])f[i+1][j+1][1]=f[i][j][0];
		}	
	}
	fac[0]=1;
	for(LL i=1;i<=n;++i)fac[i]=fac[i-1]*i%mod;
	LL ans=fac[n];
	for(LL i=1,j=-1;i<=n;++i,j=-j){
/**/	ans=(ans+mod+j*fac[n-i]*((f[tot][i][0]+f[tot][i][1])%mod)%mod)%mod;
	}
	cout<<ans<<endl;
	return 0;
}