Savings

Interview

Time limit1sMemory limit128 MB

Summary

For each test case, print how many years of multiplying the balance by (1 + B/100) are needed until it first exceeds M.

Level: Easy2 of 10
Topics: Simulation, Math, Implementation, Brute force
Solved: No attempts yet

Problem

Sanggeun opened a new bank account and deposited $N$ won. After that, he never deposits into or withdraws from this account.

Every time one full year passes since the account was opened, the bank adds interest equal to $B\%$ of the balance currently in the account. In other words, the balance is multiplied by $(1 + B / 100)$ each year.

Sanggeun wonders after how many years the balance will first exceed $M$ won.

Given $N$ , $B$ , and $M$ , write a program that determines how many years must pass for the balance to exceed $M$ won.

Input

The input consists of several test cases. Each test case is a single line containing three real numbers $N$ , $B$ , and $M$ , separated by spaces. $M$ is always greater than $N$ .

$N$ and $M$ are greater than $0$ and at most $1\,000\,000$ . $B$ is greater than $0$ and at most $50$ . Every number may be given with up to two decimal places.

The input continues until end of file (EOF).

Output

For each test case, print on its own line the number of years that must pass for the balance to exceed $M$ won.

Examples2

Example 1
Input
```
200.00 6.5 300
500 4 1000.00
```
Expected output
```
7
18
```
Example 2
Input
```
100 50 150
```
Expected output
```
2
```