Concept behind this "maths"

[Kalcor]

Captain Bill the Hummingbird and his crew recieved an interesting challenge offer. Some stranger gave them a map, potion of teleportation and said that only this potion might help them to reach the treasure.

Bottle with potion has two values x and y written on it. These values define four moves which can be performed using the potion:
(a,b) > (a + x, b + y)
(a,b) > (a + x, b - y)
(a,b) > (a - x, b + y)
(a,b) > (a - x, b - y)

Map shows that the position of Captain Bill the Hummingbird is (x1, y1) and the position of the treasure is (x2, y2).

You task is to tell Captain Bill the Hummingbird whether he should accept this challenge or decline. If it is possible for Captain to reach the treasure using the potion then output "YES", otherwise "NO" (without quotes).

The potion can be used infinite amount of times.

Input
The first line contains four integer numbers x1, y1, x2, y2 ( - 105 ≤ x1, y1, x2, y2 ≤ 105) — positions of Captain Bill the Hummingbird and treasure respectively.

The second line contains two integer numbers x, y (1 ≤ x, y ≤ 105) — values on the potion bottle.

Output
Print "YES" if it is possible for Captain to reach the treasure using the potion, otherwise print "NO" (without quotes).

Examples
input
0 0 0 6
2 3
output
YES
input
1 1 3 6
1 5
output
NO
Note
In the first example there exists such sequence of moves:

(0,0) > (2,3) — the first type of move
(2,3) > (0,6) — the third type of move

Then the editorial for the problem says:
http://prntscr.com/fku74e

Sample solution:

#include <stdio.h>

int abs(int a) {return a<0?-a:a;}

int main() {
	int a,b,c,d,x,y;
	scanf("%d%d%d%d%d%d",&a,&b,&c,&d,&x,&y);
	if (abs(a-c)%x==0 && abs(b-d)%y==0 && abs(a-c)/x%2 == abs(b-d)/y%2) printf("YES");
	else printf("NO");
}

I just don't get the maths behind this wide equation

[gunnerfunner]

OP: you deleted the actual problem from your previous post after getting help which makes the thread less informative and relevant, are you going to do the same again here?
http://www.cplusplus.com/forum/general/218121/

[Kalcor]

@gunner, it was because I received help before any replies were made to it so I forgot to delete it when I received the help and was too late so I just did it afterwards cause it was pointless to be there I am sorry if that was a wrong thing to do I just saw it being pointless cause I managed to get help before it, apologies.

[JLBorges]

> I just don't get the maths behind this wide equation

Hint:
If we start at position == 4, and if one increment x is either +2 or -2, we would be able to reach any even numbered position; but we would not be able to reach any odd numbered position.

If we start at position == 4, and if one increment x is either +3 or -3, we would be able to reach any position which is at 4 + n * 3 or 4 - n * 3 (where n is an integer); but we would not be able to reach any other position.