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>
std::vector<long long> lucky_nums;
int num = 0;
void generate_lucky() {
  lucky_nums.push_back(0);
  for (int i = 1; i < 1024; ++i) {
    long long current = i;
    long long number = 0;
    long long c_pow = 1;
    while (current) {
      long long last_d = current & 1;
      number += (last_d == 0 ? 4 : 7) * c_pow;
      c_pow *= 10;
      current >>= 1;
    }
    if (number < 0) break;
    long long symetric_num = (number - 7 * c_pow / 10) + 4 * c_pow / 10;
    lucky_nums.push_back(symetric_num);
    lucky_nums.push_back(number);
  }
  std::sort(lucky_nums.begin(), lucky_nums.end());
}
long long contain(long long x1, long long y1, long long x2, long long y2) {
  long long l = std::max(x1, x2);
  long long r = std::min(y1, y2);
  return r - l + 1 > 0 ? r - l + 1 : 0;
}
int main() {
  long long Pl, Pr, Vl, Vr;
  int k;
  std::cin >> Pl >> Pr >> Vl >> Vr >> k;
  long long sum = 0;
  generate_lucky();
  for (int i = 1; i <= 1022 - k + 1; i++) {
    int j = i + k - 1;
    sum += contain(lucky_nums[i - 1] + 1, lucky_nums[i], Pl, Pr) *
           contain(lucky_nums[j], lucky_nums[j + 1] - 1, Vl, Vr);
    if (lucky_nums[i] > Pr) break;
  }
  for (int i = 1; i <= 1022 - k + 1; i++) {
    int j = i + k - 1;
    sum += contain(lucky_nums[i - 1] + 1, lucky_nums[i], Vl, Vr) *
           contain(lucky_nums[j], lucky_nums[j + 1] - 1, Pl, Pr);
    if (lucky_nums[i] > Vr) break;
  }
  if (k == 1) {
    for (int i = 1; i <= 1022; i++) {
      if (contain(lucky_nums[i], lucky_nums[i], Pl, Pr) &&
          contain(lucky_nums[i], lucky_nums[i], Vl, Vr))
        sum--;
    }
  }
  std::cout.precision(20);
  std::cout << sum * 1.0 / (Vr - Vl + 1) / (Pr - Pl + 1);
}