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 (x₁, y₁), (x₂, y₂), ..., (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 $\text{[math]}$ relative to two points P and Q as the smallest real number d so that for all points X on line $\text{[math]}$ , |PX - QX| ≤ d. (It is guaranteed that d exists and is unique.) They wish to find the line $\text{[math]}$ passing through two distinct outposts (x_i, y_i) and (x_j, y_j) such that the difference of $\text{[math]}$ 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 $\text{[math]}$ .

Note

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

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

Armistice Area Apportionment

Examples