Hey Kakao, a word that changes daily life, is an artificial intelligence assistant application based on Kakao Enterprise's AI platform Kakao i. Using Hey Kakao, you can use various functions such as music search, directions, and foreign language translation with a single word.

According to the 2020 Hey Kakao Year-End Review, the most heard phrase by Hey Kakao after "Thank you" and "Hello" was "Let's play word chain". Yiha, who was playing with his phone in his room, decided to play word chain with Hey Kakao for fun.

Yiha played several rounds of word chain casually and gathered statistics. As a result, he found out that playing one round of word chain takes $a$ minutes, and his current probability of winning is $d\%$. Yiha was disappointed with his win rate and decided to play with focus from now on. When Yiha focuses, every time he loses a word chain game, he gains experience, and his probability of winning increases by $k\%$ compared to the previous round. If the increased probability exceeds $100\%$, Yiha is guaranteed to win from the next round onwards.

Yiha wants to play word chain until he wins against Hey Kakao once. Let's find the expected value of the time Yiha spends playing word chain.

Input

The first line contains three space-separated integers $a$, $d$, and $k$ ($1 \le a, d, k \le 100$). This means that one round of word chain takes $a$ minutes, the initial probability of Yiha winning after starting to focus is $d\%$, and every time he loses, his win rate increases by $k\%$ compared to the previous round.

All values given in the input are integers.

Output

Print the expected value of the time Yiha spends playing word chain until he wins, in minutes. The output will be accepted as correct if its absolute or relative error does not exceed $10^{-6}$.

Examples

Input 1

1 50 50

Output 1

1.6250000

Input 2

15 3 7

Output 2

226.3344692

Note

In Example 1, the probability of Yiha winning the first round is $50\%$, the probability of winning the second round after one loss is $75\%$, and finally, the probability of winning the third round is $100\%$.