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 M 924844033
ll n,k,dp[2005][2005][2],h[2005],ans,r[2005],p[4005];
void up(ll &x,ll y){x=(x+y)%M;}
int main(void){
    scanf("%lld%lld",&n,&k);
    r[0]=1;
    for(ll i=1;i<=n;i++)r[i]=r[i-1]*i%M;
    for(int i=0;i<min(n,k*2);i++){
		dp[i][0][0]=1;
		if(i>=k)dp[i][1][0]=1;
		if(i+k<n)dp[i][1][1]=1;
	}
	for(int i=0;i<n-k*2;i++){
		for(int j=0;j<=(n+k*2-1)/(k*2);j++){
			up(dp[i+k*2][j][0],dp[i][j][0]+dp[i][j][1]);
			up(dp[i+k*2][j+1][0],dp[i][j][0]);
			if(i+k*3<n)up(dp[i+k*2][j+1][1],dp[i][j][0]+dp[i][j][1]);
		}
	}
	h[0]=1;
	for(int i=max(n-k*2,0LL);i<n;i++){
		for(int j=0;j<4000;j++)p[j]=0;
		for(int j=0;j<=(n+k*2-1)/(k*2);j++){
			ll x=(dp[i][j][0]+dp[i][j][1])%M;
			for(int l=0;l<=n;l++)p[l+j]=(p[l+j]+x*h[l]%M)%M;
		}
		for(int j=0;j<=n;j++)h[j]=p[j];
	}
	for(int i=0;i<=n;i++){
		if(i%2)ans=(ans+M-r[n-i]*h[i]%M)%M;
		else ans=(ans+r[n-i]*h[i])%M;
	}
	printf("%lld\n",ans);
}