Reach a Given Number

You are given three integers: A, B, and N. Your task is to determine whether it is possible to reach the value N starting from either A or B using one of the following operations:

• Replace A with A + B.
• Replace B with A + B. If it is possible to reach N, print the minimum number of operations required. If it is not possible print NOT POSSIBLE.

Constraints

-10000000000 ≤ A, B, N ≤ 10000000000

Example 1

Input:

A = 1
B = 2
N = 5

Output:

2

Explanation: (1, 2) -> (2, 3) -> (3, 5)

Example 2

Input:

A = -1
B = 0
N = 5

Output:

"NOT POSSIBLE"

Explanation: (-1, 0) -> (-1, 0) States are either remain unchanged or produce negative value for both A and B.