Water Jug Puzzle

Given two jugs, A and B, with capacities \(C_a\) and \(C_b\) respectively, and an unlimited water supply, you are allowed to perform the following operations:

• fill A: Fill jug A to its full capacity.
• fill B: Fill jug B to its full capacity.
• empty A: Empty jug A.
• empty B: Empty jug B.
• pour A->B: Pour water from jug A into jug B. The pouring stops either when jug A becomes empty or jug B becomes full.
• pour B->A: Pour water from jug B into jug A. The pouring stops either when jug B becomes empty or jug A becomes full.

Your task is to output a sequence of valid operations that results in exactly \(N\) units of water in jug B. Note that during a pouring operation, if jug A is used to pour into jug B and either jug A runs out of water or jug B becomes full, you must immediately stop pouring.

For example, if jug A has a capacity of 5 gallons and jug B has a capacity of 6 gallons, and you start with \(8\) gallons of water in jug A, then when pouring from A to B, jug B becomes full and jug A will be left with 3 gallons.

inputFormat

The input consists of three integers \(C_a\), \(C_b\), and \(N\) separated by spaces. Here, \(C_a\) and \(C_b\) denote the capacities of jug A and jug B respectively, and \(N\) is the target amount of water that must be exactly contained in jug B.

outputFormat

Output a sequence of operations (one per line) that transforms the state such that jug B contains exactly \(N\) units of water. The allowed operations are:

• fill A
• fill B
• empty A
• empty B
• pour A->B
• pour B->A

If no sequence of operations exists, output "No solution.".

sample

5 6 4

fill A
pour A->B
fill A
pour A->B
empty B
pour A->B