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;

#define ull unsigned long long

const int Mod(924844033);
int F[2003], G[2003][2], fac[2003];

int main()
{
	int n, K, tot = 0;
	scanf("%d%d", &n, &K);
	F[0] = 1;
	for(int c = 1; c <= K * 2 && c <= n; c++)
	{
		int m = (n - c) / (2 * K) + 1;
		for(int i = 0; i <= m; i++)
			G[i][0] = G[i][1] = 0;
		G[0][c <= K] = 1;
		for(int i = 1; i <= m; i++)
			for(int j = i; ~j; j--)
			{
				int x = G[j][0], y = G[j][1];
				G[j][0] = ((x + y) % Mod + G[j - 1][0]) % Mod;
				G[j][1] = (G[j - 1][0] + G[j - 1][1]) % Mod;
			}
		if((m - 1) * 2 * K + c + K > n)
			for(int i = 1; i <= m; i++)
				G[i][1] = 0;
		tot += m;
		for(int j = tot; j; j--)
			for(int i = 1; i <= m && i <= j; i++)
				F[j] = (F[j] + (ull) F[j - i] * (G[i][0] + G[i][1])) % Mod;
	}
	for(int i = fac[0] = 1; i <= n; i++)
		fac[i] = (ull) fac[i - 1] * i % Mod;
	int ans = fac[n];
	for(int i = 1; i <= n; i++)
	{
		int x = (ull) F[i] * fac[n - i] % Mod;
		if(i & 1) ans = (ans - x + Mod) % Mod;
		else ans = (ans + x) % Mod;
	}
	printf("%d\n", ans);
	return 0;
}