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 int vl, vr, pl, pr, k, INF = 1e9 + 10;
vector<long long int> lucky;
void init() {
  long long int r;
  lucky.push_back(0);
  lucky.push_back(INF);
  for (long long int l = 1; l < 10; l++) {
    for (long long int i = 0; i < (1LL << l); i++) {
      r = 0;
      for (long long int j = 0; j < l; j++) {
        r = r * 10 + 4 + (1 & (i >> j)) * 3;
      }
      lucky.push_back(r);
    }
  }
  sort(lucky.begin(), lucky.end());
}
long long int intersect(long long int al, long long int ar, long long int bl,
                        long long int br) {
  return max(0LL, min(ar, br) - max(al, bl) + 1);
}
signed main() {
  cout << fixed << setprecision(10);
  init();
  cin >> vl >> vr >> pl >> pr >> k;
  long long int num = 0, sgn = 1, l, r;
  if (k == 1) {
    for (long long int i = 1; i < lucky.size() - k; i++) {
      l = lucky[i], r = lucky[i + k - 1];
      num += intersect(lucky[i - 1] + 1, lucky[i], vl, vr) *
             intersect(lucky[i + k - 1], lucky[i + k] - 1, pl, pr);
      num += intersect(lucky[i - 1] + 1, lucky[i], pl, pr) *
             intersect(lucky[i + k - 1], lucky[i + k] - 1, vl, vr);
      num -= intersect(lucky[i], lucky[i], pl, pr) *
             intersect(lucky[i + k - 1], lucky[i + k - 1], vl, vr);
    }
    cout << 1.0 * num / (vr - vl + 1) / (pr - pl + 1) << endl;
    return 0;
  }
  for (long long int i = 1; i < lucky.size() - k; i++) {
    l = lucky[i], r = lucky[i + k - 1];
    num += intersect(lucky[i - 1] + 1, lucky[i], vl, vr) *
           intersect(lucky[i + k - 1], lucky[i + k] - 1, pl, pr);
    num += intersect(lucky[i - 1] + 1, lucky[i], pl, pr) *
           intersect(lucky[i + k - 1], lucky[i + k] - 1, vl, vr);
  }
  cout << 1.0 * num / (vr - vl + 1) / (pr - pl + 1) << endl;
}