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 lucky[2000], lucky_count = 0;
pair<int, int> intersect(pair<int, int> a, pair<int, int> b) {
  return pair<int, int>(max(a.first, b.first), min(a.second, b.second));
}
int main() {
  long long int pl, pr, vl, vr, k;
  cin >> pl >> pr >> vl >> vr >> k;
  for (int i = 1; i <= 9; i++) {
    for (int j = 0; j < (1 << i); j++) {
      long long int num = 0;
      for (int z = 0; z < i; z++) {
        num *= 10;
        if (j & (1 << z))
          num += 7;
        else
          num += 4;
      }
      lucky[lucky_count++] = num;
    }
  }
  sort(lucky, lucky + lucky_count);
  int l = 0, r = l + k - 1;
  long long int tot = (pr - pl + 1LL) * (vr - vl + 1LL);
  long long int fav = 0;
  while (r < lucky_count) {
    for (int i = 0; i < 2; i++) {
      if (lucky[l] - pl + 1 > 0) {
        if (vr - lucky[r] + 1 > 0) {
          pair<int, int> a, b, c, s1, s2;
          a = pair<int, int>(pl, pr);
          b = pair<int, int>(pl, lucky[l]);
          c = pair<int, int>((l != 0) ? lucky[l - 1] + 1 : -100, lucky[l]);
          s1 = intersect(a, intersect(b, c));
          if (s1.first <= s1.second) {
            a = pair<int, int>(vl, vr);
            b = pair<int, int>(lucky[r], vr);
            c = pair<int, int>(lucky[r], (r != lucky_count - 1)
                                             ? lucky[r + 1] - 1
                                             : 10000000000LL);
            s2 = intersect(a, intersect(b, c));
            if (s2.first <= s2.second) {
              fav +=
                  (s1.second - s1.first + 1LL) * (s2.second - s2.first + 1LL);
            }
          }
        }
      }
      swap(pr, vr);
      swap(pl, vl);
    }
    if (k == 1 and pl <= lucky[l] and lucky[l] <= pr and vl <= lucky[l] and
        lucky[l] <= vr)
      fav--;
    r++, l++;
  }
  printf("%.12lf\n", double(fav) / double(tot));
  return 0;
}