#include <bits/stdc++.h>
using namespace std;
const double pi = acos(0.0) * 2.0;
const long double eps = 1e-10;
const int step[8][2] = {{-1, 0}, {0, 1}, {1, 0},  {0, -1},
                        {-1, 1}, {1, 1}, {1, -1}, {-1, -1}};
template <class T>
inline T abs1(T a) {
  return a < 0 ? -a : a;
}
template <typename t, typename t1>
t min1(t a, t1 b) {
  return a < b ? a : b;
}
template <typename t, typename... arg>
t min1(t a, arg... arr) {
  return min1(a, min1(arr...));
}
template <typename t, typename t1>
t max1(t a, t1 b) {
  return a > b ? a : b;
}
template <typename t, typename... arg>
t max1(t a, arg... arr) {
  return max1(a, max1(arr...));
}
inline int jud(double a, double b) {
  if (abs(a) < eps && abs(b) < eps)
    return 0;
  else if (abs1(a - b) / max(abs1(a), abs1(b)) < eps)
    return 0;
  if (a < b) return -1;
  return 1;
}
template <typename it, typename t1>
inline int find(t1 val, it a, int na, bool f_small = 1, bool f_lb = 1) {
  if (na == 0) return 0;
  int be = 0, en = na - 1;
  if (*a <= *(a + na - 1)) {
    if (f_lb == 0)
      while (be < en) {
        int mid = (be + en + 1) / 2;
        if (jud(*(a + mid), val) != 1)
          be = mid;
        else
          en = mid - 1;
      }
    else
      while (be < en) {
        int mid = (be + en) / 2;
        if (jud(*(a + mid), val) != -1)
          en = mid;
        else
          be = mid + 1;
      }
    if (f_small && jud(*(a + be), val) == 1) be--;
    if (!f_small && jud(*(a + be), val) == -1) be++;
  } else {
    if (f_lb)
      while (be < en) {
        int mid = (be + en + 1) / 2;
        if (jud(*(a + mid), val) != -1)
          be = mid;
        else
          en = mid - 1;
      }
    else
      while (be < en) {
        int mid = (be + en) / 2;
        if (jud(*(a + mid), val) != 1)
          en = mid;
        else
          be = mid + 1;
      }
    if (!f_small && jud(*(a + be), val) == -1) be--;
    if (f_small && jud(*(a + be), val) == 1) be++;
  }
  return be;
}
template <class T>
inline T lowb(T num) {
  return num & (-num);
}
inline int bitnum(unsigned int nValue) { return __builtin_popcount(nValue); }
inline int bitnum(int nValue) { return __builtin_popcount(nValue); }
inline int bitnum(unsigned long long nValue) {
  return __builtin_popcount(nValue) + __builtin_popcount(nValue >> 32);
}
inline int bitnum(long long nValue) {
  return __builtin_popcount(nValue) + __builtin_popcount(nValue >> 32);
}
inline int bitmaxl(unsigned int a) {
  if (a == 0) return 0;
  return 32 - __builtin_clz(a);
}
inline int bitmaxl(int a) {
  if (a == 0) return 0;
  return 32 - __builtin_clz(a);
}
inline int bitmaxl(unsigned long long a) {
  int temp = a >> 32;
  if (temp) return 32 - __builtin_clz(temp) + 32;
  return bitmaxl(int(a));
}
inline int bitmaxl(long long a) {
  int temp = a >> 32;
  if (temp) return 32 - __builtin_clz(temp) + 32;
  return bitmaxl(int(a));
}
long long pow(long long n, long long m, long long mod = 0) {
  if (m < 0) return 0;
  long long ans = 1;
  long long k = n;
  while (m) {
    if (m & 1) {
      ans *= k;
      if (mod) ans %= mod;
    }
    k *= k;
    if (mod) k %= mod;
    m >>= 1;
  }
  return ans;
}
template <class t1, class t2>
inline void add(t1 &a, t2 b, int mod = -1) {
  if (mod == -1) mod = 1000000007;
  a += b;
  while (a >= mod) a -= mod;
  while (a < 0) a += mod;
}
template <class t>
void output1(t arr) {
  for (int i = 0; i < (int)arr.size(); i++) cerr << arr[i] << ' ';
  cerr << endl;
}
template <class t>
void output2(t arr) {
  for (int i = 0; i < (int)arr.size(); i++) output1(arr[i]);
}
const int maxn = 100100;
pair<double, double> arr[maxn];
pair<double, double> cen;
int n, m;
pair<long double, int> inter[maxn];
int cnt[maxn], loc[maxn];
int bef[maxn], nxt[maxn];
pair<pair<double, double>, pair<double, double>> getinter(int no, double r) {
  double ra = (1 + arr[no].first * arr[no].first);
  double rb = 2 * (arr[no].second - cen.second) * arr[no].first - 2 * cen.first;
  double rc = (arr[no].second - cen.second) * (arr[no].second - cen.second) +
              cen.first * cen.first - r * r;
  if (rb * rb < 4 * ra * rc)
    return make_pair(make_pair(-1e100, -1e100), make_pair(-1e100, -1e100));
  double delta = (rb * rb - 4 * ra * rc);
  delta = sqrt(delta);
  double x1 = (-rb + delta) / 2 / ra, x2 = (-rb - delta) / 2 / ra;
  return make_pair(make_pair(x1, arr[no].first * x1 + arr[no].second),
                   make_pair(x2, arr[no].first * x2 + arr[no].second));
}
long double getang(long double x, long double y) {
  if (x == 0) {
    if (y > 0)
      return pi / 2;
    else
      return pi / 2 * 3;
  }
  if (x > 0) {
    if (y < 0)
      return atan(y / x) + pi * 2;
    else
      return atan(y / x);
  } else {
    return atan(y / x) + pi;
  }
}
template <class t>
struct tree_array {
  t num[1 << 17], n, bigwei;
  void upd(int no, t add) {
    while (no <= n) {
      num[no] += add;
      no += lowb(no);
    }
  }
  t que(int no) {
    t ans = 0;
    while (no) {
      ans += num[no];
      no -= lowb(no);
    }
    return ans;
  }
  int getrank(t x) {
    int ans = 0, ranwei = bigwei;
    t rank = 0;
    while (ranwei) {
      if (rank + num[ranwei + ans] < x) {
        ans += ranwei;
        rank += num[ans];
      }
      ranwei >>= 1;
    }
    return ans + 1;
  }
};
tree_array<int> ta;
int main() {
  ios_base::sync_with_stdio(0);
  double rtime = 0;
  scanf("%d", &n);
  scanf("%lf%lf%d", &cen.first, &cen.second, &m);
  cen.first /= 1000, cen.second /= 1000;
  for (int i = 0; i < n; i++) {
    scanf("%lf%lf", &arr[i].first, &arr[i].second);
    arr[i].first /= 1000;
    arr[i].second /= 1000;
  }
  long double be = 0, en = 1e10;
  int lin;
  for (int ii = 0; ii < 100; ii++) {
    long double mid = (be + en) / 2;
    lin = 0;
    for (int i = 0; i < n; i++) {
      pair<pair<double, double>, pair<double, double>> temp = getinter(i, mid);
      if (temp.first.first < -1e50) continue;
      inter[lin++] = make_pair(
          getang(temp.first.first - cen.first, temp.first.second - cen.second),
          i);
      inter[lin++] = make_pair(getang(temp.second.first - cen.first,
                                      temp.second.second - cen.second),
                               i);
    }
    sort(inter, inter + lin);
    memset(cnt, 0, sizeof(cnt));
    ta.n = lin + 10;
    for (int i = 0; i < lin + 10; i++) ta.num[i + 1] = 0;
    int rsum = 1;
    long long all = 0;
    for (int i = 0; i < lin; i++) {
      if (cnt[inter[i].second] == 0) {
        cnt[inter[i].second]++;
        loc[inter[i].second] = rsum;
        ta.upd(rsum, 1);
        rsum++;
      } else {
        cnt[inter[i].second]++;
        all += ta.que(rsum) - ta.que(loc[inter[i].second]);
        ta.upd(loc[inter[i].second], -1);
      }
    }
    if (all < m)
      be = mid;
    else
      en = mid;
  }
  lin = 0;
  for (int i = 0; i < n; i++) {
    pair<pair<double, double>, pair<double, double>> temp = getinter(i, be);
    if (temp.first.first < -1e50) continue;
    inter[lin++] = make_pair(
        getang(temp.first.first - cen.first, temp.first.second - cen.second),
        i);
    inter[lin++] = make_pair(
        getang(temp.second.first - cen.first, temp.second.second - cen.second),
        i);
  }
  sort(inter, inter + lin);
  memset(cnt, 0, sizeof(cnt));
  memset(bef, -1, sizeof(bef));
  memset(nxt, -1, sizeof(nxt));
  int head = -1;
  double ans = 0;
  int rcnt = 0;
  for (int i = 0; i < lin; i++) {
    int no = inter[i].second;
    if (cnt[no] == 0) {
      cnt[no]++;
      nxt[no] = head;
      if (head != -1) bef[head] = no;
      head = no;
    } else {
      double rx, ry;
      for (int j = head; j != no; j = nxt[j]) {
        rx = (arr[j].second - arr[no].second) / (arr[no].first - arr[j].first);
        ry = arr[no].first * rx + arr[no].second;
        ans += sqrt((cen.first - rx) * (cen.first - rx) +
                    (cen.second - ry) * (cen.second - ry));
        rcnt++;
      }
      if (bef[no] != -1) nxt[bef[no]] = nxt[no];
      if (nxt[no] != -1) bef[nxt[no]] = bef[no];
      if (no == head) head = nxt[head];
    }
  }
  ans += (m - rcnt) * be;
  printf("%.10f\n", ans);
  return 0;
}
