Integer Growth Until Threshold

Source: Phước Hưng OJ

Version: Phuoc Hung OJ Extended

Problem Statement

Initial integer amount a is below b. At the end of every year update a=floor(a*(100+p)/100). Count the first year reaching b; return -1 if an update makes no progress below b.

Input

Three integers a b p.

Output

Minimum number of years or -1 if unreachable.

Subtasks

• Subtask 1 (20%): 1 ≤ a < b ≤ 1000, 0 ≤ p ≤ 100.

• Subtask 2 (30%): 1 ≤ a < b ≤ 10^6, 0 ≤ p ≤ 100.

• Subtask 3 (50%): 1 ≤ a < b ≤ 10^9, 0 ≤ p ≤ 100.

Examples

Example 1

Input:

100 110 10

Output:

1

Explanation: One update gives 110, reaching the threshold.

Example 2

Input:

1 2 1

Output:

-1

Explanation: The yearly update produces no increase.

Example 3

Input:

100 120 10

Output:

2

Explanation: The amounts after years one and two are 110 and 121.