A - 迷子の高橋君 / Takahashi is Missing!

Time Limit: 2 sec / Memory Limit: 256 MB

問題文

• 青木君は、今いる座標を a とすると、a-1aa+13 箇所から移動先を選んで移動することが出来る。
• 高橋君は、今いる座標を b とすると、p パーセントの確率で b-1 に移動し、100-p パーセントの確率で b+1 に移動する。

制約

• 1x1,000,000,000
• 1p100
• x, p は整数である。

部分点

• 200 点分のデータセットでは、 p=100 が成り立つ。
• 300 点分のデータセットでは、 x10 が成り立つ。

入力

x
p


入力例 1

3
100


出力例 1

2.0000000


入力例 2

6
40


出力例 2

7.5000000


入力例 3

101
80


出力例 3

63.7500000


Score : 700 points

Problem Statement

Aoki is in search of Takahashi, who is missing in a one-dimentional world. Initially, the coordinate of Aoki is 0, and the coordinate of Takahashi is known to be x, but his coordinate afterwards cannot be known to Aoki.

Time is divided into turns. In each turn, Aoki and Takahashi take the following actions simultaneously:

• Let the current coordinate of Aoki be a, then Aoki moves to a coordinate he selects from a-1, a and a+1.

• Let the current coordinate of Takahashi be b, then Takahashi moves to the coordinate b-1 with probability of p percent, and moves to the coordinate b+1 with probability of 100-p percent.

When the coordinates of Aoki and Takahashi coincide, Aoki can find Takahashi. When they pass by each other, Aoki cannot find Takahashi.

Aoki wants to minimize the expected number of turns taken until he finds Takahashi. Find the minimum possible expected number of turns.

Constraints

• 1x1,000,000,000
• 1p100
• x and p are integers.

Partial Scores

• In the test set worth 200 points, p=100.
• In the test set worth 300 points, x10.

Input

The input is given from Standard Input in the following format:

x
p


Output

Print the minimum possible expected number of turns. The output is considered correct if the absolute or relative error is at most 10^{-6}.

Sample Input 1

3
100


Sample Output 1

2.0000000


Takahashi always moves by -1. Thus, by moving to the coordinate 1 in the 1-st turn and staying at that position in the 2-nd turn, Aoki can find Takahashi in 2 turns.

Sample Input 2

6
40


Sample Output 2

7.5000000


Sample Input 3

101
80


Sample Output 3

63.7500000