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>
#include <algorithm>

using namespace std;

typedef long long ll;

const int MAXN = 2E3 + 10;
const ll MOD = 924844033;

int n, K;
int m0;
ll a[MAXN];
int com[MAXN][MAXN];

void calc(int m){
	static ll c[MAXN];
	int m1 = m >> 1;
	copy_n(a, m0 + 1, c);
	fill_n(a, m0 + m1 + 1, 0);
	for (int i = 0; i <= m1; ++i){
		ll t = com[m - i][i];
		for (int j = 0; j <= m0; ++j)
			a[i + j] = (a[i + j] + t * c[j]) % MOD;
	}
	m0 += m1;
}

int main(){
	for (int i = 0; i < MAXN; ++i){
		com[i][0] = com[i][i] = 1;
		for (int j = 1; j < i; ++j)
			com[i][j] = (com[i - 1][j - 1] + com[i - 1] [j]) % MOD;
	}
	scanf("%d%d", &n, &K);
	a[0] = 1, m0 = 0;
	for (int i = 0; i < K; ++i){
		calc((n - i - 1) / K + 1);
		calc((n - i - 1) / K + 1);
	}
	ll ans = 0;
	ll e = n & 1 ? -1 : 1;
	for (int i = n; i >= 0; --i){
		ans = (ans + e * a[i]) % MOD;
		e = MOD - e * (n - i + 1) % MOD;
	}
	printf("%d\n", (int)ans);
	
	return 0;
}