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 <bits/stdc++.h>
using namespace std;
#define rep(i, a, b) for (int i = a; i <= b; i++)
#define per(i, a, b) for (int i = a; i >= b; i--)
typedef long long LL;
const LL mod = 924844033;
// head
const int maxn = 2005;
int n, k, cnt;
LL fac[maxn], f[maxn<<1][maxn][2], g[maxn], ans;
bool vis[maxn<<1];

int main() {
	cin>>n>>k;
	rep(i, 1, k) {
		for(int j = i; j <= n; j += k) 
			vis[++cnt] = (j == i);
		for(int j = i; j <= n; j += k)
			vis[++cnt] = (j == i);
	}
	f[0][0][0] = fac[0] = 1;
	rep(i, 1, n) fac[i] = i*fac[i - 1]%mod;
	rep(i, 1, n<<1)
	    rep(j, 0, min(i, n)) {
	    	f[i][j][0] = (f[i - 1][j][0] + f[i - 1][j][1])%mod;
	    	if(!vis[i]) f[i][j][1] = f[i - 1][j - 1][0];
	    }
	rep(i, 0, n) {
		int op = (i&1) ? -1:1;
		g[i] = (f[n<<1][i][0] + f[n<<1][i][1])%mod;
		ans = (ans + op*g[i]*fac[n - i]%mod + mod)%mod;
	}
	cout<<ans<<endl;
}