Problem G. Generations ≡

Statement

Two fathers and two sons walked together... It is well known that this could describe a group of either 3 or 4 people.

Now let's say that A fathers and B sons walked together. Could it be that this group consisted of exactly N different persons?

A person is counted as a father if there is his son among the group. A person is counted as a son if there is his father among the group. Each father can have one or more sons, each son must have exactly one father. Father of a person can not be this person's descendant. Each person must me either a son, a father, or both.

Your program must, given numbers A B N, output corresponding father-son relationship or determine that it does not exist.

Input file format

Input file contains integers A B N.

Output file format

Output file must contain a number of father-son relationships M followed by M pairs a_i b_i where a_i is a number of the father, b_i is a number of the son (1 ≤ a_i, b_i ≤ N).

All pairs must be different. If there are several solutions, output any of them. If it is impossible for a group to consist of N persons, output file must contain a single integer 0.

Constraints

1 ≤ A ≤ B ≤ 100

1 ≤ N ≤ 200

Sample tests

2 2 3

2
3 1
1 2

2 2 4

2
1 2
3 4

2 2 5

0