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;

typedef long long LL;
#define N 2200

const LL mod=924844033;
LL n,m,ans,fac[N],ifac[N],f[N][N],g[N];

void upd(LL &x,LL y){x=(x+y%mod+mod)%mod;}

void trans(LL len){
	for (LL i=n;~i;--i)
		for (LL j=1;j<=len&&j<=i;++j)
			upd(g[i],g[i-j]*f[len][j]);
}

LL inv(LL x){return x==1?1:(mod-mod/x)*inv(mod%x)%mod;}

LL C(LL x,LL y){return x<y||y<0?0:fac[x]*ifac[y]%mod*ifac[x-y]%mod;}

int main(){
	scanf("%lld%lld",&n,&m);
	fac[0]=1; for (LL i=1;i<=n;++i) fac[i]=fac[i-1]*i%mod;
	ifac[n]=inv(fac[n]); for (LL i=n-1;~i;--i) ifac[i]=ifac[i+1]*(i+1)%mod;
	f[0][0]=1;
	for (LL i=1;i<=n;++i)
		for (LL j=0;j<=i;++j)
			f[i][j]=(f[i-1][j]+(i>1&&j>0?f[i-2][j-1]:0))%mod;
	g[0]=1;
	for (LL i=1;i<=m;++i){
		LL len=(n-i)/m+1;
		trans(len); trans(len);
	}
	for (LL i=0;i<=n;++i)
		upd(ans,g[i]*fac[n-i]*(i&1?-1:1));
	printf("%lld\n",ans);
	
	return 0;
}