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;

const int maxn = 2005;
const int mod = 924844033;
int fac[maxn];
int f[maxn*2][maxn];
int a[maxn*2];

int n, k;

int main(){
	fac[0]=1;
	for(int i = 1; i < maxn; ++i)
		fac[i] = 1ll * fac[i-1] * i % mod;
	while(~scanf("%d%d", &n, &k)) {
		memset(f, 0, sizeof(f));
		int cur = 0;
		for(int j = 1; j <= k; ++j) {
			int sz = (n - j) / k + 1;
			for(int i = 0; i < sz; ++i) a[++cur] = j << 1;
			for(int i = 0; i < sz; ++i) a[++cur] = j << 1 | 1;
		}
		f[0][0] = 1;
		for(int i = 1; i <= n * 2; ++i) {
			for(int j = 0; j <= n; ++j) f[i][j] = f[i-1][j];
			if(a[i] == a[i-1])
				for(int j = 1; j <= n; ++j) (f[i][j] += f[i-2][j-1]) %= mod;
		}
		int ans = 0;
		for(int i = 0; i <= n; ++i) 
			ans = (ans + ((i & 1) ? -1ll : 1ll) * f[n<<1][i] * fac[n-i]) % mod;
		if(ans < 0) ans += mod;
		printf("%d\n", ans);
	}
}