You are given integers ~N~ and ~M~. Among all real solutions ~(a, b, c, d)~ to the equations ~a+b+c+d = N~ and ~a^2+b^2+c^2+d^2 = M~, what is the maximal value of ~d~?

Constraints

~-10^3 \le N \le 10^3~

~0 \le M \le 10^6~

Input Specification

The only line contains two space-separated integers, ~N~ and ~M~.

Output Specification

If there are no solutions, output no; otherwise, output the maximal value of ~d~.

Your answer will be accepted if the absolute error is within ~10^{-6}~.

Sample Input

7 13

Sample Output

2.500000

Explanation for Sample

The maximal value of ~d~ is reached at ~(a, b, c, d) = (1.5, 1.5, 1.5, 2.5)~.