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 <iostream>
#include <cstdio>
#include <algorithm>
#include <cstring>
#define mod 924844033
#define N 4004
#define ll long long

using namespace std;

int n, k, cnt;
ll f[N][N][2], ans, fac[N], a[N];

void init();

int main(){
	cin >> n >> k;init();
	for(int i = 1; i <= k; ++i){
		for(int j = i; j <= n; j += k) a[++cnt] = j;
		for(int j = i; j <= n; j += k) a[++cnt] = j;
	}
	f[1][0][0] = 1;
	for(int i = 2; i <= (n << 1); ++i)
		for(int j = 0; j <= min(n, i / 2); ++j){
			f[i][j][0] = (f[i - 1][j][0] + f[i - 1][j][1]) % mod;
			if(j > 0 && a[i] - a[i - 1] == k) f[i][j][1] = f[i - 1][j - 1][0];
		}
	for(int i = 0; i <= n; ++i){
		ll sum = (f[n << 1][i][0] + f[n << 1][i][1]) % mod;
		(ans += (sum * fac[n - i] % mod * ((i & 1) ? -1 : 1) + mod) % mod) %= mod;
	}
	cout << ans << endl;
	return 0;
}

void init(){
	fac[0] = 1;
	for(int i = 1; i <= 2000; ++i)
		fac[i] = fac[i - 1] * i % mod;
	return ;
}