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<stdio.h>
#include<vector>
#include<algorithm>
using namespace std;
typedef long long ll;
ll mod = 924844033;
ll dp[4001][2016][2];
int main()
{
	int num, kai;
	scanf("%d%d", &num, &kai);
	dp[0][0][0] = 1;
	int pt = 0;
	for (int i = 0; i < kai * 2; i++)
	{
		int t = 0;
		int nx, ny;
		if (i < kai)nx = i, ny = i + kai;
		else nx = i, ny = i - kai;
		for (;;)
		{
			if (nx >= num || ny >= num)break;
			t++;
			if (nx < ny)nx += kai * 2;
			else ny += kai * 2;
		}
		for (int j = 0; j < t; j++)
		{
			for (int k = 0; k <= num; k++)
			{
				dp[pt + 1][k][0] += dp[pt][k][0] + dp[pt][k][1];
				dp[pt + 1][k + 1][1] += dp[pt][k][0];
				dp[pt + 1][k][0] %= mod;
				dp[pt + 1][k + 1][1] %= mod;
			}
			pt++;
		}
		for (int k = 0; k <= num; k++)
		{
			dp[pt][k][0] += dp[pt][k][1];
			dp[pt][k][0] %= mod;
			dp[pt][k][1] = 0;
		}
	}
	ll ans = 0;
	ll now = 1;
	for (int i = num; i >= 0; i--)
	{
		if (i % 2 == 0)
		{
			ans += dp[pt][i][0] * now;
		}
		else
		{
			ans += mod - dp[pt][i][0] * now % mod;
		}
		ans %= mod;
		now *= (num - i + 1);
		now %= mod;
	}
	printf("%lld\n", ans);
}