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 pl, pr, vl, vr, k;
long long all, ans = 0;
long long masK[2000];
int kl = -1;
void pereb(long long x) {
  if (x > 1000000000) return;
  masK[++kl] = x;
  pereb(x * 10 + 4);
  pereb(x * 10 + 7);
}
long long intersection(int x, int y, int x1, int y1) {
  if (y < x1 || y1 < x) return 0;
  return abs(min(y, y1) - max(x, x1)) + 1;
}
int main() {
  cin >> pl >> pr >> vl >> vr >> k;
  all = (pr - pl + 1) * (vr - vl + 1);
  pereb(0);
  masK[kl + 1] = 1000000005;
  sort(masK + 1, masK + kl + 1);
  int i = 1, j = i + k - 1;
  while (true) {
    long long c = intersection(masK[i - 1] + 1, masK[i], pl, pr) *
                  intersection(masK[j], masK[j + 1] - 1, vl, vr);
    long long c1 = intersection(masK[i - 1] + 1, masK[i], vl, vr) *
                   intersection(masK[j], masK[j + 1] - 1, pl, pr);
    ans += c + c1;
    if (k == 1 && c && c1) ans--;
    i++;
    j = i + k - 1;
    if (j > kl) break;
  }
  printf("%0.10f", double(1.0 * ans / all));
  return 0;
}