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 <cmath>
#include <cstdio>
#include <cstring>
#include <iostream>
#include <algorithm>
using namespace std;
#define N 4005
#define ll long long
#define mod 924844033
int f[N][N][2], A[N], fac[N];
void Add(int &x, int y)
{
	x += y;
	if (x >= mod)
		x -= y;
}
int n, k;
int main()
{
	scanf("%d%d", &n, &k);
	fac[0] = 1;
	for (int i = 1; i <= n; i++)
		fac[i] = (ll)fac[i - 1] * i % mod;
	int cnt = 0;
	for (int i = 1; i <= k; i++)
	{
		for (int j = i; j <= n; j += k)
			A[++cnt] = (i == j);
		for (int j = i; j <= n; j += k)
			A[++cnt] = (i == j);
	}
	f[0][0][0] = 1;
	for (int i = 1; i <= (n << 1); i++)
		for (int j = 0; j <= i; ++j)
		{
			Add(f[i][j][0], (f[i - 1][j][0] + f[i - 1][j][1]) % mod);
			if (!A[i] && j)
				Add(f[i][j][1], f[i - 1][j - 1][0]);
		}
	int ans = 0;
	for (int i = 0; i <= n; i++)
	{
		int res = (f[n << 1][i][0] + f[n << 1][i][1]) % mod;
		if (i & 1)
			ans = (ans - (ll)res * fac[n - i]) % mod;
		else
			ans = (ans + (ll)res * fac[n - i]) % mod;
	}
	if (ans < 0)
		ans += mod;
	printf("%d\n", ans);
}