10144 - 母亲的牛奶

农民约翰有三个容量分别是A,B,C升的桶，A,B,C分别是三个从1到20的整数，最初，A和B桶都是空的，而C桶是装满牛奶的。有时，约翰把牛奶从一个桶倒到另一个桶中，直到被灌桶装满或原桶空了。当然每一次灌注都是完全的。由于节约，牛奶不会有丢失。 写一个程序去帮助约翰找出当A桶是空的时候，C桶中牛奶所剩量的所有可能性。

单独的一行包括三个整数A,B和C。

只有一行，列出当A桶是空的时候，C桶牛奶所剩量的所有可能性。

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.

PROGRAM NAME: milk3 INPUT FORMAT A single line with the three integers A, B, and C.

SAMPLE INPUT (file milk3.in) 8 9 10

OUTPUT FORMAT 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.

SAMPLE OUTPUT (file milk3.out) 1 2 8 9 10

SAMPLE INPUT (file milk3.in) 2 5 10

SAMPLE OUTPUT (file milk3.out) 5 6 7 8 9 10