#include <bits/stdc++.h>
using namespace std;
int read() {
  int x = 0, f = 1;
  char ch = getchar();
  while (ch - '0' < 0 || ch - '0' > 9) {
    if (ch == '-') f = -1;
    ch = getchar();
  }
  while (ch - '0' >= 0 && ch - '0' <= 9) {
    x = x * 10 + ch - '0';
    ch = getchar();
  }
  return x * f;
}
int n, m;
long double X, Y;
struct P {
  long double k, b;
} L[50010];
bool dcmp(long double x) { return fabs(x) < 1e-10; }
pair<long double, int> p[50010 * 2];
int ma[50010];
int cnt, top;
struct Bit {
  int t[50010 * 2];
  void init() {
    for (int i = 1; i <= top; i++) t[i] = 0;
  }
  int lowbit(int x) { return x & (-x); }
  void add(int x) {
    for (int i = x; i <= top; i += lowbit(i)) t[i]++;
  }
  int query(int x) {
    int res = 0;
    for (int i = x; i; i -= lowbit(i)) res += t[i];
    return res;
  }
} T;
void pre(long double R) {
  top = 0;
  for (int i = 1; i <= n; i++) {
    long double A = L[i].k * L[i].k + 1, B = 2 * L[i].k * L[i].b,
                C = L[i].b * L[i].b - R * R;
    if (B * B - 4 * A * C < 0) continue;
    long double tmp = sqrt(B * B - 4 * A * C);
    long double x1 = (-B + tmp) / (2 * A), y1 = L[i].k * x1 + L[i].b,
                a1 = atan2(y1, x1);
    long double x2 = (-B - tmp) / (2 * A), y2 = L[i].k * x2 + L[i].b,
                a2 = atan2(y2, x2);
    p[++top] = make_pair(a1, i);
    p[++top] = make_pair(a2, i);
  }
  for (int i = 1; i <= n; i++) ma[i] = 0;
  sort(p + 1, p + top + 1);
  for (int i = top; i >= 1; i--)
    if (!ma[p[i].second]) ma[p[i].second] = i;
}
bool check(long double R) {
  pre(R);
  T.init();
  long long res = 0;
  for (int i = 1; i <= top; i++) {
    if (ma[p[i].second] != i) {
      res += T.query(ma[p[i].second]) - T.query(i - 1);
      T.add(ma[p[i].second]);
    }
  }
  return (res >= m);
}
set<pair<int, int> > st;
long double calc(int i, int j) {
  long double x = (L[i].b - L[j].b) / (L[j].k - L[i].k),
              y = L[i].k * x + L[i].b;
  return sqrt(x * x + y * y);
}
long double solve(long double R) {
  pre(R);
  long double res = 0;
  int tot = 0;
  for (int i = 1; i <= top; i++) {
    if (ma[p[i].second] != i) {
      set<pair<int, int> >::iterator it = st.upper_bound(make_pair(i + 1, 0));
      while (it != st.end() && (it->first) < ma[p[i].second]) {
        res += calc(p[i].second, it->second);
        ++it;
        tot++;
      }
      st.insert(make_pair(ma[p[i].second], p[i].second));
    }
  }
  return res + R * (m - tot);
}
int main() {
  n = read();
  X = read() / 1000.0;
  Y = read() / 1000.0;
  m = read();
  for (int i = 1; i <= n; i++)
    L[i].k = read() / 1000.0, L[i].b = L[i].k * X + (read() / 1000.0) - Y;
  long double l = 0, r = 1e10;
  for (int i = 1; i <= 100; i++) {
    long double mid = (l + r) / 2;
    if (check(mid))
      r = mid;
    else
      l = mid;
  }
  cout << fixed << setprecision(9) << solve(l) << endl;
  return 0;
}
