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<cstdio>
#include<cstring>
#include<algorithm>
#define ll long long
using namespace std;
const int N=4010,P=924844033;
inline int read(){
	int x=0,f=0,c=getchar();
	for(;c>'9'||c<'0';f=c=='-',c=getchar());
	for(;c>='0'&&c<='9';c=getchar())
	x=(x<<1)+(x<<3)+c-'0';return f?-x:x;
}
inline void write(ll x){
	if(x<0)putchar('-'),x=-x;
	if(x>9)write(x/10);putchar(x%10+'0');
}
int n,m,i,j,sm,ed[N],f[N][N][2],v[N][2],fac[N],ans;
int dfs(int x,int k){
	v[x][k]=1;
	if(x+m<=n)return dfs(x+m,k^1)+1;
	else return 1;
}
inline void A(int&x,int y){(x+=y)%=P;}
int main(){
	n=read();m=read();
	for(i=1;i<=n;i++)
	for(j=0;j<2;j++)if(!v[i][j])
	sm+=dfs(i,j),ed[sm]=1;
	f[1][0][0]=1;
	for(i=1;i<=sm;i++)
	for(j=0;j<=n;j++){
		A(f[i+1][j][0],f[i][j][0]);
		A(f[i+1][j][0],f[i][j][1]);
		if(!ed[i])A(f[i+1][j+1][1],f[i][j][0]);
	}
	fac[0]=1;
	for(i=1;i<=n;i++)fac[i]=1ll*fac[i-1]*i%P;ans=fac[n];
	for(i=1;i<=n;i++){
		j=1ll*fac[n-i]*f[sm+1][i][0]%P;
		if(i&1)j=P-j;A(ans,j);
	}printf("%d\n",ans);
	return 0;
}