Problem: While Grisha was celebrating New Year with Ded Moroz, Misha gifted Sasha a small rectangular pond of size n × m, divided into cells of size 1 × 1, inhabited by tiny evil fishes (no more than one fish per cell, otherwise they'll strife!).

The gift bundle also includes a square scoop of size r × r, designed for fishing. If the lower-left corner of the scoop-net is located at cell (x, y), all fishes inside the square (x, y)...(x + r - 1, y + r - 1) get caught. Note that the scoop-net should lie completely inside the pond when used.

Unfortunately, Sasha is not that skilled in fishing and hence throws the scoop randomly. In order to not frustrate Sasha, Misha decided to release k fishes into the empty pond in such a way that the expected value of the number of caught fishes is as high as possible. Help Misha! In other words, put k fishes in the pond into distinct cells in such a way that when the scoop-net is placed into a random position among (n - r + 1)·(m - r + 1) possible positions, the average number of caught fishes is as high as possible.

Input

The only line contains four integers n, m, r, k (1 ≤ n, m ≤ 105, 1 ≤ r ≤ min(n, m), 1 ≤ k ≤ min(n·m, 105)).

Output

Print a single number — the maximum possible expected number of caught fishes.

You answer is considered correct, is its absolute or relative error does not exceed 10 - 9. Namely, let your answer be a, and the jury's answer be b. Your answer is considered correct, if <image>.

Examples

Input

3 3 2 3


Output

2.0000000000


Input

12 17 9 40


Output

32.8333333333

Note

In the first example you can put the fishes in cells (2, 1), (2, 2), (2, 3). In this case, for any of four possible positions of the scoop-net (highlighted with light green), the number of fishes inside is equal to two, and so is the expected value.

<image>

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
#pragma GCC target("avx2")
#pragma GCC optimization("O3")
#pragma GCC optimization("unroll-loops")
using namespace std;
template <class T1, class T2>
inline bool chmax(T1 &a, T2 b) {
  if (a < b) {
    a = b;
    return true;
  }
  return false;
}
template <class T1, class T2>
inline bool chmin(T1 &a, T2 b) {
  if (a > b) {
    a = b;
    return true;
  }
  return false;
}
const double EPS = 1e-9, PI = acos(-1);
const double pi = 3.141592653589793238462643383279;
template <int mod>
struct ModInt {
  int x;
  ModInt() : x(0) {}
  ModInt(int64_t y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {}
  ModInt &operator+=(const ModInt &p) {
    if ((x += p.x) >= mod) x -= mod;
    return *this;
  }
  ModInt &operator-=(const ModInt &p) {
    if ((x += mod - p.x) >= mod) x -= mod;
    return *this;
  }
  ModInt &operator*=(const ModInt &p) {
    x = (int)(1LL * x * p.x % mod);
    return *this;
  }
  ModInt &operator/=(const ModInt &p) {
    *this *= p.inverse();
    return *this;
  }
  ModInt operator-() const { return ModInt(-x); }
  ModInt operator+(const ModInt &p) const { return ModInt(*this) += p; }
  ModInt operator-(const ModInt &p) const { return ModInt(*this) -= p; }
  ModInt operator*(const ModInt &p) const { return ModInt(*this) *= p; }
  ModInt operator/(const ModInt &p) const { return ModInt(*this) /= p; }
  bool operator==(const ModInt &p) const { return x == p.x; }
  bool operator!=(const ModInt &p) const { return x != p.x; }
  ModInt inverse() const {
    int a = x, b = mod, u = 1, v = 0, t;
    while (b > 0) {
      t = a / b;
      swap(a -= t * b, b);
      swap(u -= t * v, v);
    }
    return ModInt(u);
  }
  ModInt pow(int64_t n) const {
    ModInt ret(1), mul(x);
    while (n > 0) {
      if (n & 1) ret *= mul;
      mul *= mul;
      n >>= 1;
    }
    return ret;
  }
  friend ostream &operator<<(ostream &os, const ModInt &p) { return os << p.x; }
  friend istream &operator>>(istream &is, ModInt &a) {
    int64_t t;
    is >> t;
    a = ModInt<mod>(t);
    return (is);
  }
  static int get_mod() { return mod; }
};
using modint = ModInt<998244353>;
template <typename T>
struct Combination {
  vector<T> _fact, _rfact, _inv;
  Combination(int sz) : _fact(sz + 1), _rfact(sz + 1), _inv(sz + 1) {
    _fact[0] = _rfact[sz] = _inv[0] = 1;
    for (int i = 1; i <= sz; i++) _fact[i] = _fact[i - 1] * i;
    _rfact[sz] /= _fact[sz];
    for (int i = sz - 1; i >= 0; i--) _rfact[i] = _rfact[i + 1] * (i + 1);
    for (int i = 1; i <= sz; i++) _inv[i] = _rfact[i] * _fact[i - 1];
  }
  inline T fact(int k) const { return _fact[k]; }
  inline T rfact(int k) const { return _rfact[k]; }
  inline T inv(int k) const { return _inv[k]; }
  T P(int n, int r) const {
    if (r < 0 || n < r) return 0;
    return fact(n) * rfact(n - r);
  }
  T C(int p, int q) const {
    if (q < 0 || p < q) return 0;
    return fact(p) * rfact(q) * rfact(p - q);
  }
  T H(int n, int r) const {
    if (n < 0 || r < 0) return (0);
    return r == 0 ? 1 : C(n + r - 1, r);
  }
};
long long GCD(long long a, long long b) { return (b == 0) ? a : GCD(b, a % b); }
long long LCM(long long a, long long b) { return a / GCD(a, b) * b; }
long long H, W, r, k;
long long calc(long long y, long long x) {
  long long t1 = 0, t2 = 0;
  if (0 <= y && y < r && H - r <= y && y < H) {
    t1 += H - r + 1;
  } else if (0 <= y && y < r) {
    t1 += y + 1;
  } else if (H - r <= y && y < H) {
    t1 += H - y;
  } else {
    t1 += r;
  }
  if (0 <= x && x < r && W - r <= x && x < W) {
    t2 += W - r + 1;
  } else if (0 <= x && x < r) {
    t2 += x + 1;
  } else if (W - r <= x && x < W) {
    t2 += W - x;
  } else {
    t2 += r;
  }
  return t1 * t2;
}
int dxy[5] = {-1, 0, 1, 0, -1};
int main() {
  cin.tie(0);
  ios::sync_with_stdio(false);
  cout << fixed << setprecision(12);
  cin >> H >> W >> r >> k;
  long long ans = 0;
  priority_queue<pair<long long, long long>> pq;
  long long sy = H / 2, sx = W / 2;
  pq.push({calc(sy, sx), sy * W + sx});
  set<long long> st;
  st.insert(sy * W + sx);
  long long t = 0;
  while (t < k && pq.size()) {
    auto p = pq.top();
    pq.pop();
    ans += p.first;
    t++;
    int y = p.second / W, x = p.second % W;
    if (pq.size() >= k * 10) {
      continue;
    }
    for (int i = 0; i < 4; i++) {
      long long ny = y + dxy[i], nx = x + dxy[i + 1];
      if (ny >= 0 && ny < H && nx >= 0 && nx < W) {
        if (st.find(ny * W + nx) != st.end()) continue;
        pq.push({calc(ny, nx), ny * W + nx});
        st.insert(ny * W + nx);
      }
    }
  }
  cout << (double)(ans) / (double)((H - r + 1) * (W - r + 1)) << endl;
  return 0;
}