Buildings

Your current task is to make a ground plan for a residential building located in HZXJHS. So you must determine a way to split the floor building with walls to make apartments in the shape of a rectangle. Each built wall must be paralled to the building‘s sides.

The floor is represented in the ground plan as a large rectangle with dimensions n×m, where each apartment is a smaller rectangle with dimensions a×b located inside. For each apartment, its dimensions can be different from each other. The numbera and b must be integers.

Additionally, the apartments must completely cover the floor without one 1×1 square located on (x,y). The apartments must not intersect, but they can touch.

For this example, this is a sample of n=2,m=3,x=2,y=2.



To prevent darkness indoors, the apartments must have windows. Therefore, each apartment must share its at least one side with the edge of the rectangle representing the floor so it is possible to place a window.

Your boss XXY wants to minimize the maximum areas of all apartments, now it‘s your turn to tell him the answer.

There are at most 10000 testcases.
For each testcase, only four space-separated integers, n,m,x,y(1≤n,m≤108,n×m>1,1≤x≤n,1≤y≤m).

2 3 2 2
3 3 1 1

1
2

Hint
Case 1 :

You can split the floor into five $1 \times 1$ apartments. The answer is 1.

Case 2:
 
You can split the floor into three $2 \times 1$ apartments and two $1\times 1$ apartments. The answer is 2.

  
If you want to split the floor into eight $1 \times 1$ apartments, it will be unacceptable because the apartment located on (2,2) can‘t have windows.
 

假设没有坏点 ans=(min(n,m)+1)/2

假设n=m=奇数，x,y在中间 ans‘=(min(n,m)+1)/2-1

否则，x,y用对称性挪到左上角

此时对于宿舍楼要么竖着分max(y,m-y+1)+1

要么横着分 min(x,n-x+1)

#include<cstdio>
#include<cstring>
#include<cstdlib>
#include<algorithm>
#include<functional>
#include<iostream>
#include<cmath>
#include<cctype>
#include<ctime>
using namespace std;
#define For(i,n) for(int i=1;i<=n;i++)
#define Fork(i,k,n) for(int i=k;i<=n;i++)
#define Rep(i,n) for(int i=0;i<n;i++)
#define ForD(i,n) for(int i=n;i;i--)
#define RepD(i,n) for(int i=n;i>=0;i--)
#define Forp(x) for(int p=pre[x];p;p=next[p])
#define Forpiter(x) for(int &p=iter[x];p;p=next[p])  
#define Lson (x<<1)
#define Rson ((x<<1)+1)
#define MEM(a) memset(a,0,sizeof(a));
#define MEMI(a) memset(a,127,sizeof(a));
#define MEMi(a) memset(a,128,sizeof(a));
#define INF (2139062143)
#define F (100000007)
typedef long long ll;
ll mul(ll a,ll b){return (a*b)%F;}
ll add(ll a,ll b){return (a+b)%F;}
ll sub(ll a,ll b){return (a-b+llabs(a-b)/F*F+F)%F;}
void upd(ll &a,ll b){a=(a%F+b%F)%F;}
int main()
{
//	freopen("B.in","r",stdin);
	
	int n,m,x,y;
	while(scanf("%d%d%d%d",&n,&m,&x,&y)==4) {
		if (n<m) swap(n,m),swap(x,y);
		
		int ans=(min(n,m)+1)/2;
		if (n==m&&x==y&&n==2*x-1) 
		{
			cout<<ans-1<<endl; continue;
		} 
		
		x=min(x,n-x+1),y=max(y,m-y+1);
		
		int ans2=min(x,y-1);
		
		cout<<max(ans2,ans)<<endl; 
		
	}	
	
	
	return 0;
}