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;
#pragma GCC optimize("O2,no-stack-protector,unroll-loops,fast-math")
#define F first
#define S second
#define pb push_back
#define SZ(x) (ll)(x.size())
#define all(x) x.begin(),x.end()
#define MP make_pair
typedef long long ll;
typedef long double ld;
typedef pair<ll,ll> pll;
const ll maxn=2e3+10, maxm=2e5+500, lg=19, mod=924844033, inf=1e18;

ll n,k,dp[maxn][2],fac[maxn];

int main(){
	ios_base::sync_with_stdio(0),cin.tie(0),cout.tie(0);
	
	fac[0]=1; for(int i=1;i<maxn;i++) fac[i]=fac[i-1]*i%mod;
	cin>>n>>k;
	dp[0][0]=1;
	for(int i=1;i<=min(n,k);i++)for(int T:{0,1}){
		for(int j=1;j<=(n-i)/k;j++)for(int l=n;l>=0;l--){
			(dp[l][0]+=dp[l][1])%=mod;
			if(l) dp[l][1]=dp[l-1][0];
		}
		for(int j=0;j<=n;j++) (dp[j][0]+=dp[j][1])%=mod, dp[j][1]=0;
	}
	ll ans=0;
	for(int i=0;i<=n;i++) ans=(ans+(i%2 ? -1:+1)*(dp[i][0]*fac[n-i]%mod)+mod)%mod;
	cout<<ans;
	
	return 0;
}