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;

const int MOD = 924844033;
int N , K , C[2003][2003] , dp[2003] , jc[2003];

int main(){
	cin >> N >> K;
	C[0][0] = 1;
	for(int i = 1 ; i <= N ; ++i){
		C[i][0] = 1;
		for(int j = 1 ; j <= N ; ++j)
			C[i][j] = (C[i - 1][j] + C[i - 1][j - 1]) % MOD;
	}
	dp[0] = 1; int all = 0;
	for(int i = 1 ; i <= 2 * K && i <= N ; ++i){
		int sum = 0;
		for(int j = i ; j <= N ; j += 2 * K) sum += (j - K > 0) + (j + K <= N);
		for(int j = all ; j >= 0 ; --j)
			for(int k = (sum + 1) / 2 ; k ; --k)
				dp[j + k] = (dp[j + k] + 1ll * dp[j] * C[sum - k + 1][k]) % MOD;
		all += (sum + 1) / 2;
	}
	jc[0] = 1; for(int i = 1 ; i <= N ; ++i) jc[i] = 1ll * jc[i - 1] * i % MOD;
	for(int i = 0 ; i <= N ; ++i) dp[i] = 1ll * dp[i] * jc[N - i] % MOD;
	int ans = 0; for(int i = 0 ; i <= N ; ++i) ans = (ans + (i & 1 ? -1ll : 1ll) * dp[i] + MOD) % MOD;
	cout << ans; return 0;
}