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 lucky[1111];
int cnt, k;
void dfs(int digit, int i, int Lnumber) {
  if (i == digit) {
    ++cnt;
    lucky[cnt] = Lnumber;
    return;
  }
  dfs(digit, i + 1, Lnumber * 10 + 4);
  dfs(digit, i + 1, Lnumber * 10 + 7);
}
long long intersection(long long x1, long long y1, long long x2, long long y2) {
  long long l = max(x1, x2);
  long long r = min(y1, y2);
  if (r - l + 1 > 0)
    return r - l + 1;
  else
    return 0;
}
int main() {
  for (int digit = 1; digit <= 9; digit++) dfs(digit, 0, 0);
  lucky[0] = 0;
  ++cnt;
  lucky[cnt] = 1000000000;
  long long Pl, Pr, Vl, Vr;
  scanf("%lld%lld%lld%lld%d", &Pl, &Pr, &Vl, &Vr, &k);
  long long sum = 0;
  for (int i = 1; i <= 1022 - k + 1; i++) {
    int j = i + k - 1;
    sum += intersection(lucky[i - 1] + 1, lucky[i], Pl, Pr) *
           intersection(lucky[j], lucky[j + 1] - 1, Vl, Vr);
    if (lucky[i] > Pr) break;
  }
  for (int i = 1; i <= 1022 - k + 1; i++) {
    int j = i + k - 1;
    sum += intersection(lucky[i - 1] + 1, lucky[i], Vl, Vr) *
           intersection(lucky[j], lucky[j + 1] - 1, Pl, Pr);
    if (lucky[i] > Vr) break;
  }
  if (k == 1) {
    for (int i = 1; i <= 1022; i++) {
      sum -= (intersection(lucky[i], lucky[i], Pl, Pr) *
              intersection(lucky[i], lucky[i], Vl, Vr));
    }
  }
  cout << fixed << setprecision(10)
       << (sum * 1.0) / (Vr - Vl + 1) / (Pr - Pl + 1) << endl;
}