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 long long mod=924844033;
const long long MAXN=4010;
long long n,k,a[MAXN],cnt=0,fac[MAXN],dp[MAXN][MAXN][2];
int main(){
	scanf("%lld%lld",&n,&k);
	fac[0]=1ll;for(register int i=1;i<=n;i++) fac[i]=1ll*fac[i-1]*i%mod;
	a[0]=MAXN;
	for(register int i=1;i<=k;i++){
		for(register int j=i;j<=n;j+=k) a[++cnt]=j;
		for(register int j=i;j<=n;j+=k) a[++cnt]=j;
	}	
	dp[0][0][0]=1;
	for(register int i=1;i<=(n<<1);i++){
		for(register int j=0;j<=i/2;j++){
			dp[i][j][0]=(dp[i-1][j][0]+dp[i-1][j][1])%mod;
			if(j && a[i]-a[i-1]==k)dp[i][j][1]=dp[i-1][j-1][0];
		}
	}
	long long ans=0;
	for(register int i=0;i<=n;i++){
		long long aim=(dp[n<<1][i][0]+dp[n<<1][i][1])%mod*fac[n-i]%mod;
		if(i&1) ans=((ans-aim)%mod+mod)%mod;
		else ans=(ans+aim)%mod;
	}
	printf("%lld\n",ans);
	return 0;
}