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<cstdio>
typedef long long LL;
const int MOD=924844033;
const int N=2003;

int n,k,cnt,ans;
int f[2*N][N][2];
int g[N],A[2*N],jc[N];

int main() {
	scanf("%d %d",&n,&k);
	jc[0]=1;
	for(LL i=1;i<=n;i++)
		jc[i]=i*jc[i-1]%MOD;
	for(int i=1;i<=k;i++) {
		for(int j=i;j<=n;j+=k) A[++cnt]=(i==j);
		for(int j=i;j<=n;j+=k) A[++cnt]=(i==j);
	}//加入链 
	f[0][0][0]=1;
	for(int i=1;i<=(n<<1);i++)
		for(int j=0;j<=i&&j<=n;j++) {
			f[i][j][0]=(f[i-1][j][0]+f[i-1][j][1])%MOD;
			if(!A[i]&&j) f[i][j][1]=f[i-1][j-1][0];
		}
	for(int i=0;i<=n;i++)
		g[i]=(f[n<<1][i][0]+f[n<<1][i][1])%MOD;
	for(LL i=0,o=1;i<=n;i++,o=-o)
		ans=(ans+o*g[i]*jc[n-i])%MOD;
	printf("%d\n",(ans+MOD)%MOD);
	return 0;
}