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 $(a,b,c,d)=(1.5,1.5,1.5,2.5)$.