Since UCup is also short on heads, and the AI for generating the next-next problem did not perform as expected, the Fish King Qingyu retrained a New AI.

The Fish King Qingyu's New AI refuses to work 996 hours, so it demands that Qingyu play a game with it first.

The player plays a monster-fighting game where the player has $n$ health points and the monster has $m$ health points.

At any moment, the player can choose one of the following two operations:

1. (Attack): The player performs an attack skill, which requires $1$ unit of time for cooldown. After the cooldown, the attack succeeds with probability $p$, reducing the monster's health by $1$. With probability $1-p$, the attack fails, reducing the player's health by $1$.
2. (Restart): The player gives up the current round and decides to restart. This operation takes no time, and the player's health is restored to $n$, while the monster's health is restored to $m$.

When the player's health reaches $0$, the player dies and must choose to restart. When the monster's health reaches $0$, the player wins.

Qingyu wants to know: if the player adopts the optimal strategy, what is the expected time required for the player to win?

Since Qingyu's playing time cannot exceed $10^9$ units of time, if the player cannot win after $10^9$ units of time, output $10^9$.

Input

The input consists of a single line containing three integers $n, m, c$, where $p = \displaystyle \frac{c}{100}$.

Output

Output a single real number representing the minimum of the answer and $10^9$.

Your answer will be considered correct if its relative or absolute error does not exceed $10^{-6}$.

Examples

Input 1

2 1 10

Output 1

10.0

Note 1

Since the monster only has $1$ health point, the answer is the expected number of attack rounds to kill the monster, which is $1/p = 10$. Note that since restarting takes no time, the player's death does not affect the answer.

Input 2

2 2 1

Output 2

5125.12562814070456340687

Input 3

50 60 99

Output 3

60.60606060606060606355

Input 4

114 514 19

Output 4

1000000000.00000000000000000000

Subtasks

This problem uses bundled testing; you must pass all test cases in a subtask to receive points for that subtask.

For all data, $1 \leq n,m \leq 1\,000$ and $0 < c < 100$. The detailed constraints are as follows: