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;

const int N=2010,Mod=924844033;

int n,k,P[N],f[N<<1][N][2],g[N],fact[N];
bool use[N<<1],ed[N<<1];

void Init() { scanf("%d%d",&n,&k); }

void Solve()
{
	int len=0;
	for (int i=1;i<=n;++i)
		for (int j=0;j<2;++j)
			if (!use[i<<1|j])
			{
				for (int x=i,op=j;x<=n;x+=k,op^=1)
					use[x<<1|op]=1,++len;
				ed[len]=1;
			}
	
	f[0][0][1]=1;
	for (int i=1;i<=2*n;++i)
		for (int j=0;j<=i/2;++j)
		{
			f[i][j][0]=(f[i-1][j][1]+f[i-1][j][0])%Mod;
			if (!ed[i-1] && j) f[i][j][1]=f[i-1][j-1][0];
		}
	for (int i=0;i<=n;++i)
		g[i]=(f[n<<1][i][0]+f[n<<1][i][1])%Mod;
	
	fact[0]=1; for (int i=1;i<=n;++i) fact[i]=1ll*fact[i-1]*i%Mod;
	
	LL ans=0;int op=1; 
	for (int i=0;i<=n;++i,op=-op)
		ans=(ans+1ll*g[i]*fact[n-i]*op%Mod+Mod)%Mod;
	
	printf("%lld\n",ans);
}

int main()
{
	Init();
	Solve();
	return 0;
}