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>
#define mod 924844033
#define maxn 2010
using namespace std;
int ans,dp[2][maxn][4],p=0,np=1,fac[maxn]={1},n,k;
void upd(int& x,int y){if((x+=y)>=mod)x-=mod;}
int main(){
	scanf("%d%d",&n,&k);
	for(int i=1;i<=n;++i)
		fac[i]=1ll*fac[i-1]*i%mod;
	dp[np][0][0]=1;
	for(int i=1;i<=k;++i){
		for(int j=i;j<=n;j+=k,swap(p,np))
			for(int l=0;l<=n;++l)
				for(int x=0;x<4;++x)if(dp[np][l][x]){
					int s=dp[np][l][x];
					upd(dp[p][l][x>>1],s);
					if(l+1<=n){
						if((~x&1)&&j>i)upd(dp[p][l+1][x>>1],s);
						upd(dp[p][l+1][x>>1|2],s);
					}
					dp[np][l][x]=0;
				}
		for(int l=0;l<=n;++l){
			upd(dp[np][l][0],dp[np][l][1]);
			for(int x=1;x<4;++x)dp[np][l][x]=0;
		}
	}
	for(int i=0,j=1;i<=n;++i,j=-j)
		ans=(ans+1ll*j*fac[n-i]*dp[np][i][0])%mod;//,printf("{%d}",dp[np][i][0]);
	ans=(ans+mod)%mod;
	printf("%d",ans);
}