Problem: Petya loves lucky numbers. We all know that lucky numbers are the positive integers whose decimal representations contain only the lucky digits 4 and 7. For example, numbers 47, 744, 4 are lucky and 5, 17, 467 are not.

Petya and his friend Vasya play an interesting game. Petya randomly chooses an integer p from the interval [pl, pr] and Vasya chooses an integer v from the interval [vl, vr] (also randomly). Both players choose their integers equiprobably. Find the probability that the interval [min(v, p), max(v, p)] contains exactly k lucky numbers.

Input

The single line contains five integers pl, pr, vl, vr and k (1 ≤ pl ≤ pr ≤ 109, 1 ≤ vl ≤ vr ≤ 109, 1 ≤ k ≤ 1000).

Output

On the single line print the result with an absolute error of no more than 10 - 9.

Examples

Input

1 10 1 10 2


Output

0.320000000000


Input

5 6 8 10 1


Output

1.000000000000

Note

Consider that [a, b] denotes an interval of integers; this interval includes the boundaries. That is, <image>

In first case there are 32 suitable pairs: (1, 7), (1, 8), (1, 9), (1, 10), (2, 7), (2, 8), (2, 9), (2, 10), (3, 7), (3, 8), (3, 9), (3, 10), (4, 7), (4, 8), (4, 9), (4, 10), (7, 1), (7, 2), (7, 3), (7, 4), (8, 1), (8, 2), (8, 3), (8, 4), (9, 1), (9, 2), (9, 3), (9, 4), (10, 1), (10, 2), (10, 3), (10, 4). Total number of possible pairs is 10·10 = 100, so answer is 32 / 100.

In second case Petya always get number less than Vasya and the only lucky 7 is between this numbers, so there will be always 1 lucky number.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
#pragma GCC optimize("O2")
#pragma comment(linker, "/STACK:16777216")
using namespace std;
const int N = 1001, INF = 100000000;
vector<int> vec;
int len;
void dfs(int cur, int v) {
  if (cur == 9) {
    return;
  }
  vec.push_back(v * 10 + 4);
  vec.push_back(v * 10 + 7);
  dfs(cur + 1, v * 10 + 4);
  dfs(cur + 1, v * 10 + 7);
}
long long insect(long long a, long long b, long long x, long long y) {
  if (b < x || y < a) return 0;
  long long up = min(b, y);
  long long low = max(a, x);
  return up - low + 1;
}
long long pr, pl, vr, vl, k;
long long cal(int b, int e) {
  long long res = 0;
  long long up, low, u, v;
  if (b)
    low = vec[b - 1] + 1;
  else
    low = 1;
  up = vec[b];
  u = insect(low, up, pl, pr);
  low = vec[e];
  if (e == len - 1)
    up = 1000000000;
  else
    up = vec[e + 1] - 1;
  v = insect(low, up, vl, vr);
  res += u * v;
  if (b)
    low = vec[b - 1] + 1;
  else
    low = 1;
  up = vec[b];
  u = insect(low, up, vl, vr);
  low = vec[e];
  if (e == len - 1)
    up = 1000000000;
  else
    up = vec[e + 1] - 1;
  v = insect(low, up, pl, pr);
  res += u * v;
  return res;
}
int main() {
  vec.clear();
  dfs(0, 0);
  sort(vec.begin(), vec.end());
  len = vec.size();
  while (cin >> pl >> pr >> vl >> vr >> k) {
    long long ans = 0;
    for (int i = 0; i + k - 1 < len; ++i) {
      ans += cal(i, i + k - 1);
    }
    if (k == 1)
      for (int i = 0; i < len; ++i)
        if (vec[i] <= pr && vec[i] >= pl && vec[i] <= vr && vec[i] >= vl) --ans;
    double res = ans * 1.0 / (pr - pl + 1) / (vr - vl + 1);
    printf("%.9lf\n", res);
  }
}