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 int N = 4054, mod = 924844033;

int n, K, L = 0;
int sp[N], fact[N];
int f[N][N], g[N][N];

inline void add(int &x, const int y) {x += y - mod, x += x >> 31 & mod;}

int main() {
	int i, j, c; ll ans = 0;
	scanf("%d%d", &n, &K);
	for (*fact = i = 1; i <= n; ++i) fact[i] = (ll)fact[i - 1] * i % mod;
	for (i = 0; i < K; ++i)
		sp[++L] = 1, L += (n - i - 1) / K,
		sp[++L] = 1, L += (n - i - 1) / K;
	assert(L == 2 * n);
	for (**f = i = 1; i <= L; ++i)
		for (*f[i] = j = 1; j <= (i + 1) / 2; ++j)
			add(f[i][j] = f[i - 1][j], g[i - 1][j]),
			g[i][j] = (sp[i] ? 0 : f[i - 1][j - 1]);
	for (i = 0; i <= n; ++i)
		c = ll(f[L][i] + g[L][i]) * fact[n - i] % mod,
		i & 1 ? ans -= c : ans += c;
	ans %= mod, printf("%d\n", int(ans + (ans >> 63 & mod)));
	return 0;
}