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;

typedef long long ll;

const int MAXN = 2e3 + 10;
const int MOD = 924844033;

int n, k, sz, sec[MAXN * 2];
ll c[MAXN][MAXN], ss[MAXN];
ll d[MAXN * 2];

int main(){
	ss[0] = 1;
	for (int i = 1; i < MAXN; i++)
		ss[i] = ss[i - 1] * i % MOD;

	c[0][0] = 1;
	for (int i = 1; i < MAXN; i++){
		c[i][0] = 1;
		c[i][1] = i;
		for (int j = 2; j <= i; j++)
			c[i][j] = (c[i - 1][j] + c[i - 2][j - 1]) % MOD;
	}

	cin >> n >> k;
	for (int i = 0; i < k; i++)
		if (i + k < n){
			int temp = (n - 1 - i)/ k;
			sec[sz++] = temp;
			sec[sz++] = temp;
		}

	d[0] = 1;
	for (int i = 0; i < sz; i++)
		for (int j = MAXN * 2 - 1; ~j; j--)
			for (int w = 1; w <= sec[i] && w <= j; w++)
				d[j] = (d[j] + d[j - w] * c[sec[i]][w]) % MOD;
	
	ll ans = 0;
	for (int i = 1; i <= n; i++){
		if (i & 1)
			ans = (ans + d[i] * ss[n - i] % MOD) % MOD;
		else
			ans = (ans + MOD - d[i] * ss[n - i] % MOD) % MOD;
	}
	
	cout << (ss[n] - ans + MOD) % MOD << endl;
	return 0;
}