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;
long long overlap(long long i1, long long i2, long long j1, long long j2) {
  return max(min(j2, i2) - max(j1, i1) + 1, 0LL);
}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  long long pl, pr, vl, vr, k;
  cin >> pl >> pr >> vl >> vr >> k;
  vector<long long> lucky;
  lucky.push_back(0);
  for (int i = 1; i <= 9; i++) {
    for (int j = 0; j < 1 << i; j++) {
      long long cur = 0;
      for (int k = i - 1; k >= 0; k--) {
        if ((1 << k) & j) {
          cur = 10 * cur + 7;
        } else {
          cur = 10 * cur + 4;
        }
      }
      if (cur >= min(pl, vl) && cur <= max(pr, vr)) {
        lucky.push_back(cur);
      }
    }
  }
  lucky.push_back(1e18);
  long double num = 0, den = (pr - pl + 1) * (vr - vl + 1);
  for (int i = 1; i < lucky.size(); i++) {
    long long x = overlap(pl, pr, lucky[i - 1] + 1, lucky[i] - 1), y = 0;
    if (i + k < lucky.size()) {
      y += overlap(vl, vr, lucky[i + k - 1], lucky[i + k] - 1);
    }
    if (i - k > 0) {
      y += overlap(vl, vr, lucky[i - k - 1] + 1, lucky[i - k]);
    }
    num += x * y;
  }
  for (int i = 0; i < lucky.size(); i++) {
    if (pl <= lucky[i] && lucky[i] <= pr) {
      if (i + k < lucky.size()) {
        num += overlap(vl, vr, lucky[i + k - 1], lucky[i + k] - 1);
      }
      if (i - k >= 0) {
        num += overlap(vl, vr, lucky[i - k] + 1, lucky[i - k + 1]);
      }
      if (k == 1) {
        num--;
      }
    }
  }
  cout << fixed << setprecision(12) << num / den << '\n';
  return 0;
}