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>
#define rep(i,n)for(int i=0;i<(n);i++)
#define MOD 924844033
using namespace std;
typedef long long ll;

int dp[3000][3000][2];
ll fact[3000];

int main(){
	fact[0]=1;
	for(int i=1;i<3000;i++)fact[i]=(fact[i-1]*i)%MOD;
	int n,K;scanf("%d%d",&n,&K);
	map<int,vector<int>>mp;
	rep(i,n){
		mp[i%(2*K)].push_back(i);
	}
	dp[0][0][0]=1;
	int cnt=0;
	for(auto p:mp){
		for(int i=cnt;i<cnt+p.second.size();i++)rep(j,n+1)rep(k,2){
			if(dp[i][j][k]==0)continue;
			int d=p.second[i-cnt];
			if(d+K<n)(dp[i+1][j+1][i-cnt==p.second.size()-1?0:1]+=dp[i][j][k])%=MOD;
			if(k==0&&d-K>=0)(dp[i+1][j+1][0]+=dp[i][j][k])%=MOD;
			(dp[i+1][j][0]+=dp[i][j][k])%=MOD;
		}
		cnt+=p.second.size();
	}
	int ans=0;
	for(int i=1;i<=n;i++){
		int sum=(dp[n][i][0]+dp[n][i][1])*fact[n-i]%MOD;
		if(i&1)(ans+=sum)%=MOD;
		else ans=(ans+MOD-sum)%MOD;
	}
	cout<<(fact[n]+MOD-ans)%MOD<<endl;
}