A farmer has a land in shape of rectangle has size nxm. He wants to divides his land to give to his k sons (labeled from 1 to k). Dividing process splits the land into smaller equal squares with length 1.
At first, each son will choose 1 square (No one choose same square as others). One son will expand his land by adding others square, which have same edge with their squares collected before in turn by their label until all squares are owned. It means that, they will turn around by their label to expand their land: Son with label 1 will choose first, continue with label 2,…. After label k chose, it turns again to label 1 until all squares are chosen.
Taking it faster, you suggest that you will determine number squares of each son has after this process.

Input
The first line of the input contains three positive integers n and m and k, where n,m ≤ 10⁵ is the size of the land, and 2 ≤ k ≤ 10 is number of son. Next k lines each line i^th contain 2 positive integers u and v that describe the location of first square of son i^th by index of row and column.
Output
Output k respective lines with number of squares of each son.

Sample input	Sample output
4 7 3 1 2 3 6 4 3	11 12 5

Explanation for sample