【CodeForces - 124D】Squares （旋转坐标系，计算几何，思维）

题干：

You are given an infinite checkered field. You should get from a square (x1; y1) to a square (x2; y2). Using the shortest path is not necessary. You can move on the field squares in four directions. That is, when you are positioned in any square, you can move to any other side-neighboring one.

A square (x; y) is considered bad, if at least one of the two conditions is fulfilled:

• |x + y| ≡ 0 (mod 2a),
• |x - y| ≡ 0 (mod 2b).

Your task is to find the minimum number of bad cells one will have to visit on the way from (x1; y1) to (x2; y2).

Input

The only line contains integers a, b, x1, y1, x2 and y2 — the parameters of the bad squares, the coordinates of the initial and the final squares correspondingly (2 ≤ a, b ≤ 109 and |x1|,|y1|,|x2|,|y2| ≤ 109). It is guaranteed that the initial and the final square aren't bad.

Output

Print a single number — the minimum number of bad cells that one will have to visit in order to travel from square (x1; y1) to square (x2; y2).

Examples

Input

2 2 1 0 0 1

Output

1

Input

2 2 10 11 0 1

Output

5

Input

2 4 3 -1 3 7

Output

2

Note

In the third sample one of the possible paths in (3;-1)->(3;0)->(3;1)->(3;2)->(4;2)->(4;3)->(4;4)->(4;5)->(4;6)->(4;7)->(3;7). Squares (3;1) and (4;4) are bad.

题目大意：

   给你两个平面内的点，坐标可能很大，但是不会超过int，在平面内可以上下左右走，问你从( x1 , y1 )走到( x2 , y2 )最少可能经过坏点的数量（坏点即为满足| x + y | % 2a ==0 或者| x - y | % 2b == 0） 

解题报告：

   本题想要坏点最少，而坏点所在的直线其实是满足一定规律的，就是等间距分布。
画到这里其实就已经很明显了，要使两点之间的路线坏点最少，肯定就是在这些直线之间尽量多的走交点，这里还要注意一个问题，就是跨象限的问题（x+y=0 和 x-y=0）。

题解

AC代码：

#include
using namespace std;
int a,b,x1,y1,x2,y2;
int x,y;
int main()
{
//	cout << (5/-2)<>a>>b>>x1>>y1>>x2>>y2;
	//向左旋转45°建立坐标系 ，精彩 
	x=x1;
	y=y1;
	x1=x+y;
	y1=y-x;
	
	x=x2;
	y=y2;
	x2=x+y;
	y2=y-x;
	
	a*=2;
	b*=2;
	//看是否都大于0，处理坐标轴那一点 
	x1=x1/a+(x1>0);
	x2=x2/a+(x2>0);
	y1=y1/b+(y1>0);
	y2=y2/b+(y2>0);
	//只走交点，也就是，看横着的线和竖着的线哪个多，走哪个，另外一个肯定顺便就能走完了， 
	cout<