Drunk

Jenny is seriously drunk. He feels as if he is in an N-dimension Euclidean space, wandering aimlessly. In each step, he walks toward some direction and the “length” of each step will not exceed R. Technically speaking, Jenny is initially located at the origin of the N-dimension Euclidean space. Each step can be represented by a random N-dimension vector(x₁, x₂, ... , x_n) chosen uniformly from possible positions satisfying x_i >= 0 and x₁² + x₂² + ... <= R².
Assume the expectation of his coordinate after his first step is (y₁, y₂, ... , y_n). He wants to know the minimum y_i .

There are several (about 100,000) test cases, please process till EOF.
Each test case, only one line contains two integers N and R, representing the dimension of the space and the length limit of each step.(1 <= n <= 2 * 10⁵, R <= 10⁵).

For each test case, print a real number representing the answer to the question above.
Your answer is considered correct if the difference between your answer and the correct one is less than 10^-6.

2 1

0.4244131816

2013ACM/ICPC亚洲区南京站现场赛——题目重现