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<cstring>
#include<cstdio>
#include<algorithm>
#define int long long
#define mod 924844033
using namespace std;
inline int read(){
	int f=1,ans=0;char c=getchar();
	while(c<'0'||c>'9'){if(c=='-')f=-1;c=getchar();}
	while(c>='0'&&c<='9'){ans=ans*10+c-'0';c=getchar();}
	return f*ans;
}
const int MAXN=2001;
int a[MAXN<<1],f[MAXN<<1][MAXN][2],n,k,fac[MAXN];
signed main(){
//	freopen("1.in","r",stdin);
	n=read(),k=read();
	fac[0]=1;for(int i=1;i<=n;i++) fac[i]=(fac[i-1]*i)%mod;
	for(int i=1;i<=k;i++){
		for(int j=i;j<=n;j+=k) a[++a[0]]=(i!=j);
		for(int j=i;j<=n;j+=k) a[++a[0]]=(i!=j);
	}
	f[0][0][0]=1;
	for(int i=1;i<=a[0];i++)
		for(int j=0;j<=n;j++){
			f[i][j][0]=f[i-1][j][0]+f[i-1][j][1],f[i][j][0]%=mod;
			if(j&&a[i]) f[i][j][1]=f[i-1][j-1][0],f[i][j][1]%=mod;
		}
	int pw=1,ans=0;
	for(int i=0;i<=n;i++)
		ans+=pw*fac[n-i]*((f[a[0]][i][0]+f[a[0]][i][1])%mod),pw*=-1,ans=((ans%mod)+mod)%mod;
	printf("%lld\n",ans);
}