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>
using namespace std;

typedef long long ll;

const ll mod = 924844033;
const int MAXN = 2010;

ll f[2][2][MAXN][MAXN], g[MAXN];

int main(){
	int N, K, M;
	scanf("%d %d", &N, &K);
	M = N / K + 1;
	f[1][0][0][0] = 1;
	for (int i = 1; i <= M; ++i){
		f[0][0][i][0] = 1;
		for (int j = 1; j <= i; ++j){
			f[0][0][i][j] = (f[1][0][i - 1][j] + f[0][0][i - 1][j] + f[0][0][i - 1][j - 1]) % mod;
			f[0][1][i][j] = (f[1][0][i - 1][j - 1] + f[0][0][i - 1][j - 1]) % mod;
			f[1][0][i][j] = (f[0][1][i - 1][j - 1] + f[1][1][i - 1][j] + f[0][1][i - 1][j]) % mod;
			f[1][1][i][j] = (f[0][1][i - 1][j - 1] + f[1][1][i - 1][j - 1]) % mod;
		}
	}
	g[0] = 1;
	for (int i = 1, d, t; i <= K; ++i){
		d = (N - i) / K + 1;
		for (int j = N; j >= 1; --j)
			for (int k = 1; k <= d && k <= j; ++k){
				t = (f[0][0][d][k] + f[1][0][d][k]) % mod;
				g[j] = (g[j] + g[j - k] * t % mod) % mod;
			}
	}
	ll ans = g[N], fac = 1;
	for (int i = N - 1; i >= 0; --i){
		fac = fac * (N - i) % mod;
		if (i & 1)
			ans = (ans + mod - fac * g[i] % mod) % mod;
		else
			ans = (ans + fac * g[i] % mod) % mod;
	}
	printf("%lld", ans);
	return 0;
}