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>
#include <cstring>
#include <algorithm>
#include <set>
using namespace std;
#define N 4050
#define mod 924844033
typedef long long ll;
int n,K,vis[N][2],ed[N];
int f[N][N>>1][2],g[N];
ll fac[N],ans;
int main() {
	scanf("%d%d",&n,&K);
	int i,j,x,y,cnt=0;
	for(i=1;i<=n;i++) {
		for(j=0;j<2;j++) if(!vis[i][j]) {
			for(x=i,y=j;x<=n;x+=K,y=!y) {
				vis[x][y]=1; cnt++;
			}
			ed[cnt]=1;
		}
	}
	f[1][0][0]=1;
	for(i=1;i<=cnt;i++) {
		for(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];
			}
		}
	}
	for(i=0;i<=n;i++) g[i]=(f[cnt][i][0]+f[cnt][i][1])%mod;
	for(fac[0]=i=1;i<=n;i++) fac[i]=fac[i-1]*i%mod;
	for(i=0;i<=n;i++) {
		if(i&1) ans=(ans-g[i]*fac[n-i])%mod;
		else ans=(ans+g[i]*fac[n-i])%mod;
	}
	printf("%lld\n",(ans+mod)%mod);
}