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>

typedef long long ll;

const ll kMod = 924844033;
const int kN = 2e3 + 5;

int n, k; ll f[kN << 1][kN][2], fac[kN];
bool bk[kN << 1];

int main() {
	scanf("%d%d", &n, &k);
	fac[0] = 1;
	for(int i = 1; i <= n; ++i) fac[i] = fac[i - 1] * i % kMod;
	for(int i = 0, cnt = 1; i < k; ++i) {
		bk[cnt += (n - i - 1) / k + 1] = true;
		bk[cnt += (n - i - 1) / k + 1] = true;
	}
	for(int i = 1; i <= n << 1; ++i) {
		f[i][0][0] = 1;
		for(int j = 1; j <= n; ++j) {
			f[i][j][0] = (f[i - 1][j][0] + f[i - 1][j][1]) % kMod;
			if(!bk[i]) f[i][j][1] = f[i - 1][j - 1][0];
		}
	}
	ll ans = 0, tmp = kMod - 1;
	for(int i = 1; i <= n; ++i) {
		ans = (ans + (f[n << 1][i][0] + f[n << 1][i][1]) % kMod * tmp % kMod * fac[n - i] % kMod) % kMod;
		tmp = tmp * (kMod - 1) % kMod;
	}
	printf("%lld", (fac[n] + ans) % kMod);
	return 0;
}