题目描述

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.

输入格式

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

输出格式

  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.

样例数据1

input

8 9 10

output

1 2 8 9 10

样例数据2

input

2 5 10

output

5 6 7 8 9 10