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>
#define ll long long
#define mod 924844033
#define N 4010
using namespace std;
int n, k, jc[N], inv[N], L[N], f[N], g[N], m, top, x, ans;
inline int C(int n, int m){return (ll)jc[n]*inv[m]%mod*inv[n-m]%mod;}
int main(){
	scanf("%d%d", &n, &k); m=k*2;
	jc[0]=1; for(int i=1; i<=n; i++)jc[i]=(ll)jc[i-1]*i%mod;
	inv[0]=inv[1]=1; for(int i=2; i<=n; i++)inv[i]=(ll)(mod-mod/i)*inv[mod%i]%mod;
	for(int i=1; i<=n; i++)inv[i]=(ll)inv[i-1]*inv[i]%mod;
	for(int i=1; i<=k; i++)L[i*2-1]=L[i*2]=(n-i)/k;
	memset(f, 0, sizeof(f)); f[0]=1; top=0;
	for(int i=1; i<=m; i++){
		memcpy(g, f, sizeof(g)); memset(f, 0, sizeof(f));
		for(int j=0; j<=(L[i]+1)/2; j++){
			x=C(L[i]-j+1, j);
			for(int ii=0; ii<=top; ii++)f[ii+j]=(f[ii+j]+(ll)g[ii]*x%mod)%mod;
		}
		top+=(L[i]+1)/2;
	}
	ans=0;
	for(int i=0; i<=n; i++)
		if(i&1)ans=(ans-(ll)f[i]*jc[n-i]%mod+mod)%mod;
		else ans=(ans+(ll)f[i]*jc[n-i]%mod)%mod;
	printf("%d", ans);
	return 0;
}