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>
using namespace std;
const long double EPS = 1e-10;
const long long MOD = 1e9 + 7;
const long double PI = 3.1415926535897932384626433832795028841;
long long powmod(long long a, long long b) {
  long long res = 1;
  a %= MOD;
  for (; b; b >>= 1) {
    if (b & 1) res = res * a % MOD;
    a = a * a % MOD;
  }
  return res;
}
ostream& operator<<(std::ostream& stream, const long long* arr) {
  int i = 0;
  cout << "{";
  while (arr[i] != INT_MAX) {
    cout << arr[i];
    if (arr[i + 1] != INT_MAX) cout << ",";
    i++;
  }
  cout << "}";
  return stream;
}
ostream& operator<<(std::ostream& stream, const vector<int> vec) {
  cout << "{";
  for (int i = 0; i < vec.size(); i++) {
    cout << vec[i];
    if (i != vec.size() - 1) cout << ",";
  }
  cout << "}";
  return stream;
}
ostream& operator<<(std::ostream& stream,
                    const pair<long long, long long>& vec) {
  cout << "(" << vec.first << ',' << vec.second << ")";
  return stream;
}
template <class T>
struct segtree_t {
  vector<T> t, lazy, flag_equal;
  int st, sz;
  T (*addition_fun)(T, T);
  T invalid_value;
  segtree_t() {}
  segtree_t(int start, int finish, T* arr, T (*add_fun)(T, T), T invalid_val) {
    int size = (finish + 1) * 2;
    int tree_size = 2;
    while (tree_size < size) tree_size *= 2;
    t = vector<T>(tree_size);
    lazy = vector<T>(tree_size);
    flag_equal = vector<T>(tree_size);
    st = start;
    sz = finish;
    addition_fun = add_fun;
    invalid_value = invalid_val;
    build(1, start, finish, arr);
  }
  void build(int i, int l, int r, T* arr) {
    if (l > r) return;
    lazy[i] = 0;
    flag_equal[i] = 0;
    if (l == r) {
      t[i] = arr[l];
    } else {
      build(i * 2, l, (l + r) / 2, arr);
      build(i * 2 + 1, (l + r) / 2 + 1, r, arr);
      t[i] = addition_fun(t[i * 2], t[i * 2 + 1]);
    }
  }
  void inc_range(int l, int r, T value) {
    if (l > r) return;
    inc_range_rec(1, st, sz, l, r, value);
  }
  void set_values(int l, int r, T value) {
    set_values_rec(1, st, sz, l, r, value);
  }
  void inc_range_rec(int i, int l, int r, int tl, int tr, T value) {
    if (lazy[i] != 0) {
      t[i] += lazy[i];
      if (l != r) {
        lazy[i * 2] += lazy[i];
        lazy[i * 2 + 1] += lazy[i];
      }
      lazy[i] = 0;
    }
    if (r < tl or l > tr) return;
    if (l > r) return;
    if (l >= tl and r <= tr) {
      if (l != r) {
        lazy[i * 2] += value;
        lazy[i * 2 + 1] += value;
      }
      t[i] += value;
    } else {
      inc_range_rec(i * 2, l, (l + r) / 2, tl, tr, value);
      inc_range_rec(i * 2 + 1, (l + r) / 2 + 1, r, tl, tr, value);
      t[i] = addition_fun(t[i * 2], t[i * 2 + 1]);
    }
  }
  T query_rec(int i, int l, int r, int tl, int tr) {
    if (flag_equal[i] != 0) {
      if (l != r) {
        t[i * 2] = t[i];
        t[i * 2 + 1] = t[i];
        flag_equal[i * 2] = 1;
        flag_equal[i * 2 + 1] = 1;
      }
      flag_equal[i] = 0;
    }
    if (r < tl or l > tr) return invalid_value;
    if (l > r) return invalid_value;
    if (lazy[i] != 0) {
      t[i] += lazy[i];
      if (l != r) {
        lazy[i * 2] += lazy[i];
        lazy[i * 2 + 1] += lazy[i];
      }
      lazy[i] = 0;
    }
    if (l >= tl and r <= tr) {
      return t[i];
    } else {
      T m1 = query_rec(i * 2, l, (l + r) / 2, tl, tr);
      T m2 = query_rec(i * 2 + 1, (l + r) / 2 + 1, r, tl, tr);
      if (m1 == invalid_value && m2 == invalid_value) return invalid_value;
      if (m1 == invalid_value) return m2;
      if (m2 == invalid_value) return m1;
      return addition_fun(m1, m2);
    }
  }
  T query(int l, int r) { return query_rec(1, st, sz, l, r); }
  void set_values_rec(int i, int l, int r, int tl, int tr, T value) {
    if (flag_equal[i] != 0) {
      if (l != r) {
        t[i * 2] = t[i];
        t[i * 2 + 1] = t[i];
        flag_equal[i * 2] = 1;
        flag_equal[i * 2 + 1] = 1;
      }
      flag_equal[i] = 0;
    }
    if (r < tl || l > tr) return;
    if (l > r) return;
    if (l >= tl and r <= tr) {
      t[i] = value;
      flag_equal[i] = 1;
    } else {
      set_values_rec(i * 2, l, (l + r) / 2, tl, tr, value);
      set_values_rec(i * 2 + 1, (l + r) / 2 + 1, r, tl, tr, value);
      t[i] = addition_fun(t[i * 2], t[i * 2 + 1]);
    }
  }
  ~segtree_t() {}
};
template <class T>
struct fenwick_t {
  vector<T> FW;
  fenwick_t(int n) { FW = vector<T>(n + 1); }
  void inc(int i, T v) {
    while (i <= FW.size() - 1) {
      FW[i] += v;
      i += i & (-i);
    }
  }
  T get(int i) {
    T rta = 0;
    while (i > 0) {
      rta += FW[i];
      i -= i & (-i);
    }
    return rta;
  }
};
struct dsu_t {
  vector<int> p, sz, depth;
  dsu_t() {}
  dsu_t(int n) {
    p = vector<int>(n + 1);
    sz = vector<int>(n + 1);
    depth = vector<int>(n + 1);
    for (int i = 1; i <= n; i++) {
      p[i] = i;
      sz[i] = 1;
      depth[i] = 1;
    }
  }
  int get(int i) {
    int j = i;
    while (p[i] != i) i = p[i];
    while (p[j] != j) {
      int aux = p[j];
      p[j] = i;
      j = aux;
    }
    return i;
  }
  void merge(int a, int b) {
    a = get(a);
    b = get(b);
    if (a == b) return;
    if (sz[a] > sz[b]) {
      p[b] = a;
      sz[a] += sz[b];
    } else {
      p[a] = b;
      sz[b] += sz[a];
      if (depth[a] == depth[b]) depth[b]++;
    }
  }
  void show() {
    for (int i = 1; i <= p.size() - 1; i++) {
      cout << i << ": " << p[i] << ' ' << sz[i] << ' ' << depth[i] << " \n";
    }
  }
};
const int maxn = 2 * 1e5 + 5;
const int maxm = 1e5 + 5;
const int maxk = 1e5 + 5;
const int maxq = 1e5 + 5;
long long n, m, r, k;
set<pair<long long, long long>> done;
long long fr(pair<long long, long long> v) {
  long long i = v.first;
  long long j = v.second;
  long long ca = min(i, n - r + 1LL) - max(1LL, i - r + 1LL) + 1LL;
  long long cb = min(j, m - r + 1LL) - max(1LL, j - r + 1LL) + 1LL;
  return ca * cb;
}
struct cmp {
  bool operator()(pair<long long, long long> a, pair<long long, long long> b) {
    return fr(a) < fr(b);
  }
};
priority_queue<pair<long long, long long>, vector<pair<long long, long long>>,
               cmp>
    cand;
long long dx[4] = {1, 0, -1, 0};
long long dy[4] = {0, 1, 0, -1};
void check_cand(long long i, long long j) {
  if (i < 1 || j < 1 || i > n || j > m) return;
  if (done.find(pair<long long, long long>(i, j)) != done.end()) return;
  done.insert(pair<long long, long long>(i, j));
  cand.push(pair<long long, long long>(i, j));
}
int main() {
  cin >> n >> m >> r >> k;
  check_cand(n / 2, m / 2);
  check_cand(n / 2 + 1, m / 2);
  check_cand(n / 2 + 1, m / 2 + 1);
  check_cand(n / 2, m / 2 + 1);
  long long total = 0;
  while (k--) {
    pair<long long, long long> tp = cand.top();
    cand.pop();
    done.insert(tp);
    for (int j = 0; j < 4; j++) {
      long long ny = tp.first + dy[j];
      long long nx = tp.second + dx[j];
      check_cand(ny, nx);
    }
    total += fr(tp);
  }
  double ans = double(total) / (double(n - r + 1) * double(m - r + 1));
  cout << fixed << setprecision(20) << ans << '\n';
}