After a drawn-out mooclear arms race, Farmer John and the Mischievous Mess Makers have finally agreed to establish peace. They plan to divide the territory of Bovinia with a line passing through at least two of the $*n*$ outposts scattered throughout the land. These outposts, remnants of the conflict, are located at the points $(*x*_{1}, *y*_{1}), (*x*_{2}, *y*_{2}), ..., (*x*_{*n*}, *y*_{*n*})$.

In order to find the optimal dividing line, Farmer John and Elsie have plotted a map of Bovinia on the coordinate plane. Farmer John's farm and the Mischievous Mess Makers' base are located at the points $*P* = (*a*, 0)$ and $*Q* = ( - *a*, 0)$, respectively. Because they seek a lasting peace, Farmer John and Elsie would like to minimize the maximum difference between the distances from any point on the line to $*P*$ and $*Q*$.

Formally, define the difference of a line relative to two points $*P*$ and $*Q*$ as the smallest real number $*d*$ so that for all points $*X*$ on line , $|*PX* - *QX*| ≤ *d*$. (It is guaranteed that $*d*$ exists and is unique.) They wish to find the line passing through two distinct outposts $(*x*_{*i*}, *y*_{*i*})$ and $(*x*_{*j*}, *y*_{*j*})$ such that the difference of relative to $*P*$ and $*Q*$ is minimized.

Input

The first line of the input contains two integers $*n*$ and $*a*$ ($2 ≤ *n* ≤ 100 000$, $1 ≤ *a* ≤ 10 000$) — the number of outposts and the coordinates of the farm and the base, respectively.

The following $*n*$ lines describe the locations of the outposts as pairs of integers $(*x*_{*i*}, *y*_{*i*})$ ($|*x*_{*i*}|, |*y*_{*i*}| ≤ 10 000$). These points are distinct from each other as well as from $*P*$ and $*Q*$.

Output

Print a single real number—the difference of the optimal dividing line. Your answer will be considered correct if its absolute or relative error does not exceed $10^{ - 6}$.

Namely: let's assume that your answer is $*a*$, and the answer of the jury is $*b*$. The checker program will consider your answer correct, if .

Note

In the first sample case, the only possible line is $*y* = *x* - 1$. It can be shown that the point $*X*$ which maximizes $|*PX* - *QX*|$ is $(13, 12)$, with , which is .

In the second sample case, if we pick the points $(0, 1)$ and $(0,  - 3)$, we get as $*x* = 0$. Because $*PX* = *QX*$ on this line, the minimum possible difference is $0$.