Migrated from Lutece 185 Mother's Milk

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Description

Farmer John has three milking buckets of capacity $A$, $B$, and $C$ liters. Each of the numbers $A$, $B$, and $C$ is an integer from $1$ through $20$, inclusive. Initially, buckets $A$ and $B$ are empty while bucket $C$ is full of milk. Sometimes, FJ pours milk from one bucket to another until the second bucket is filled or the first bucket is empty. Once begun, a pour must be completed, of course. Being thrifty, no milk may be tossed out.

Write a program to help FJ determine what amounts of milk he can leave in bucket $C$ when he begins with three buckets as above, pours milk among the buckets for a while, and then notes that bucket $A$ is empty.

Input

A single line with the three integers $A$, $B$, and $C$.

Output

A single line with a sorted list of all the possible amounts of milk that can be in bucket $C$ when bucket $A$ is empty.

Samples

8 9 10

1 2 8 9 10

Resources

USACO TRAINING selected by rectaflex