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>
using namespace std;
const int maxn = 1000 * 1000 * 1000;
int pl, pr, vl, vr, k;
void read_info() { cin >> pl >> pr >> vl >> vr >> k; }
vector<long long int> nums;
void make(long long int cur) {
  if (cur > maxn) return;
  nums.push_back(cur);
  make(cur * 10 + 4);
  make(cur * 10 + 7);
}
inline int intersect(int l1, int r1, int l2, int r2) {
  return max(0, min(r1, r2) - max(l1, l2) + 1);
}
int main() {
  read_info();
  make(0);
  nums.push_back(maxn);
  sort(nums.begin(), nums.end());
  int n = nums.size();
  long long count = 0;
  for (int i = 1; i < n - k; i++) {
    int l1 = nums[i - 1] + 1, r1 = nums[i];
    int l2 = nums[i + k - 1], r2 = nums[i + k] - 1;
    long long len1 = intersect(l1, r1, vl, vr);
    long long len2 = intersect(l2, r2, pl, pr);
    long long len3 = intersect(l2, r2, vl, vr);
    long long len4 = intersect(l1, r1, pl, pr);
    count += (len1) * (len2);
    count += (len3) * (len4);
    if (k == 1 && r1 >= max(vl, pl) && r1 <= min(vr, pr)) count--;
  }
  cout.precision(20);
  cout << 1.0 * count / (pr - pl + 1) / (vr - vl + 1) << endl;
  return 0;
}