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.
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