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;
template<class T> inline bool chkmax(T& a,T b){return a<b?a=b,1:0;}
template<class T> inline bool chkmin(T& a,T b){return a>b?a=b,1:0;}
template<typename T> inline T& read(T& x){
    static char c; bool flag=0;
    while(!isdigit(c=getchar())) if(c=='-') flag=1;
    for(x=c-'0';isdigit(c=getchar());(x*=10)+=c-'0');
    if(flag) x=-x;
    return x;
}
const int mo=924844033,maxn=2010;
int n,k;
int fac[maxn],f[maxn<<1][maxn][2],len,ans;
bool vis[maxn][2],flag[maxn<<1];
int main(){
	read(n); read(k);
	fac[0]=1;
	for(int i=1;i<=n;i++) fac[i]=1ll*fac[i-1]*i%mo;
	for(int i=1;i<=n;i++)
		for(int j=0;j<2;j++) if(!vis[i][j]){
			vis[i][j]=1;
			int p=i,side=j;
			while(p<=n){
				p+=k; side^=1; ++len;
				if(p<=n) vis[p][side]=1;
			}
			flag[len]=1;
		}
	f[0][0][1]=1;
	for(int i=1;i<=len;i++)
		for(int j=0;j<=n;j++){
			if(j&&!flag[i-1]) f[i][j][1]=f[i-1][j-1][0];
			f[i][j][0]=(f[i-1][j][0]+f[i-1][j][1])%mo;
		}
	for(int i=0;i<=n;i++) (ans+=1ll*((i&1)?-1:1)*(f[len][i][0]+f[len][i][1])%mo*fac[n-i]%mo)%=mo;
	cout<<(ans%mo+mo)%mo<<endl;
	return 0;
}