Problem: 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), ..., (xn, yn).

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 <image> relative to two points P and Q as the smallest real number d so that for all points X on line <image>, |PX - QX| ≤ d. (It is guaranteed that d exists and is unique.) They wish to find the line <image> passing through two distinct outposts (xi, yi) and (xj, yj) such that the difference of <image> 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 (xi, yi) (|xi|, |yi| ≤ 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 <image>.

Examples

Input

2 5
1 0
2 1


Output

7.2111025509


Input

3 6
0 1
2 5
0 -3


Output

0.0000000000

Note

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

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

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
#pragma warning(disable : 4996)
using namespace std;
int IT_MAX = 1 << 17;
const long long MOD = 987654321;
const int INF = 1034567890;
const long long LL_INF = 3234567890123456789ll;
const double PI = acos(-1);
const long double ERR = 1E-10;
inline long double sq(long double a) { return a * a; }
class Circle {
 public:
  long double x, y, r;
  Circle() { *this = Circle(0, 0, 0); }
  Circle(int X, int Y, long double R) { x = X, y = Y, r = R; }
  pair<long double, long double> meets(Circle k) {
    long double d = sqrt(sq(x - k.x) + sq(y - k.y));
    if (d + ERR > r + k.r) return pair<long double, long double>(0, -1);
    if (d < abs(r - k.r) + ERR) return pair<long double, long double>(0, -1);
    long double rt = atan2(k.y - y, k.x - x);
    long double u = acos((d * d + r * r - k.r * k.r) / (2 * d * r));
    long double r1 = rt - u;
    long double r2 = rt + u;
    if (r1 < 0) r1 += 2 * PI;
    if (r2 < 0) r2 += 2 * PI;
    if (r1 >= 2 * PI) r1 -= 2 * PI;
    if (r2 >= 2 * PI) r2 -= 2 * PI;
    if (r1 > r2) swap(r1, r2);
    return pair<long double, long double>(r1, r2);
  }
};
int in[100050][2];
vector<pair<long double, long double> > V;
vector<pair<int, int> > V2;
map<long double, int> Mx;
int bit[600000];
void update(int p, int v) {
  for (; p <= IT_MAX; p += p & (-p)) bit[p] += v;
}
int getsum(int p) {
  int rv = 0;
  for (; p > 0; p -= p & (-p)) rv += bit[p];
  return rv;
}
int main() {
  int N, A, i;
  scanf("%d %d", &N, &A);
  for (i = 1; i <= N; i++) scanf("%d %d", &in[i][0], &in[i][1]);
  long double st = ERR, en = 2 * A, mi;
  for (int iter = 1; iter <= 100; iter++) {
    mi = (st + en) / 2;
    V.clear();
    V2.clear();
    Mx.clear();
    Circle c = Circle(A, 0, mi);
    for (i = 1; i <= N; i++) {
      Circle u =
          Circle(in[i][0], in[i][1], sqrt(sq(in[i][0] + A) + sq(in[i][1])));
      pair<long double, long double> rv = c.meets(u);
      if (rv.first > rv.second) continue;
      V.push_back(pair<long double, long double>(rv.first, rv.second));
      Mx[rv.first] = 0;
      Mx[rv.second] = 0;
    }
    i = 1;
    for (auto &it : Mx) it.second = i++;
    for (auto it : V) V2.push_back(pair<int, int>(Mx[it.first], Mx[it.second]));
    sort(V2.begin(), V2.end());
    for (IT_MAX = 2; IT_MAX < i; IT_MAX *= 2)
      ;
    for (i = 1; i <= IT_MAX; i++) bit[i] = 0;
    for (i = 0; i < V2.size(); i++) {
      int rv = getsum(V2[i].second) - getsum(V2[i].first - 1);
      if (rv != 0) break;
      update(V2[i].second, 1);
    }
    if (i < V2.size())
      en = mi;
    else
      st = mi;
  }
  printf("%.20lf\n", (double)mi);
  return 0;
}