Bishop Tour

Interview

Time limit1sMemory limit512 MB

Summary

Given a board and two squares, decide whether a bishop can travel from the start square to the end square using any number of diagonal moves.

Level: Easy2 of 10
Topics: Math, Implementation, Geometry
Solved: No attempts yet

Problem

A knight's tour is a problem of finding a path on a chessboard where a knight visits every square exactly once. Chess master Heeja wondered whether the bishop, another minor piece, can also travel freely across the board. Given a start point and an end point, determine whether the bishop can move from the start point to the end point using as many moves as needed.

A bishop moves any number of squares diagonally in a single move.

Input

The first line gives the board dimensions $N$ and $M$ .

The second line gives the coordinates of the start point $(s_x, s_y)$ .

The third line gives the coordinates of the end point $(e_x, e_y)$ .

The top-left corner of the board has coordinates $(1, 1)$ , and the bottom-right corner has coordinates $(N, M)$ .

Output

Print YES if the bishop can move from the start point to the end point, or NO otherwise.

Constraints

$1 ≤ N, M ≤ 10^9$
$1 ≤ s_x, e_x ≤ N$
$1 ≤ s_y, e_y ≤ M$

Examples2

Example 1
Input
```
2 3
1 1
1 3
```
Expected output
```
YES
```
Example 2
Input
```
2 2
1 1
1 2
```
Expected output
```
NO
```