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<algorithm>
#include<cstdio>
#include<cstdlib>
#include<cstring>
using namespace std;

typedef long long ll;
const ll maxn=2e3+10,mod=924844033;
ll n,k,dp[maxn][maxn][2],ans;

int main(){
	ios::sync_with_stdio(false);
	cin>>n>>k;
	dp[0][0][0]=1;
	for(ll i=1,cnt=0;i<=2*k;++i)
		for(ll j=i;j<=n;j+=2*k){
			++cnt;
			dp[cnt][0][0]=1;
			for(ll a=1;a<=cnt;++a){
				dp[cnt][a][0]=(dp[cnt-1][a][0]+dp[cnt-1][a][1])%mod;
				if(j>k)
					(dp[cnt][a][0]+=dp[cnt-1][a-1][0])%=mod;
				if(j+2*k<=n)
					(dp[cnt][a][1]+=dp[cnt-1][a-1][0]+dp[cnt-1][a-1][1])%=mod;
				else if(j+k<=n)
					(dp[cnt][a][0]+=dp[cnt-1][a-1][0]+dp[cnt-1][a-1][1])%=mod;
			}
		}
	for(ll i=0;i<=n;++i){
		ll res=i&1?mod-1:1;
		res=res*dp[n][i][0]%mod;
		for(ll j=1;j<=n-i;++j)
			res=res*j%mod;
		(ans+=res)%=mod;
	}
	cout<<ans<<endl;
	return 0;
}