# Cut Board

# Cut Board

A rectangular board of size **n** * **m** has **1** * **1** cells. **x** consecutive cells from the first row starting from the top-left and **y** consecutive cells from the last row starting from the bottom-right are cut off. Can you fill all the cells of the remaining board using some **2** * **1** dominoes such that none overlap or hang off the edge?

Write the program which takes in four integers **n**, **m**, **x** and **y** and prints whether the remaining board can be filled with dominoes, and if yes, prints one way to place the dominoes.

#### Input

Consists of a single line containing four space-separated integers **n**, **m**, **x** and **y** (**3** ≤ **n**, **m** ≤ **100**, **1** ≤ **x**, **y** < **m**).

#### Output

Print **NO** in a single line if you cannot fill all the cells of the cut board using dominoes.

Otherwise, print **YES** in the first line, and a single integer in the second line denoting the number of dominoes required.

In the next lines, print four space-separated integers denoting the location of the domino. The **x**-coordinate corresponds to the row number and the **y**-coordinate corresponds to the column number.

If the location of domino is `x`

, _{1}`y`

, _{1}`x`

, _{2}`y`

then it is present at cells (_{2}`x`

, _{1}`y`

) and (_{1}`x`

, _{2}`y`

)._{2}

You can fill the board by placing each domino either vertically or horizontally.

If there are multiple solutions, you can output any of them.

3 4 1 3

YES 4 2 1 3 1 2 2 2 3 1 2 1 3 1 4 2 4

3 3 2 2

NO