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;
std::vector<int> luckynums;
void bt(int num, int idx, int n) {
  if (idx == n) {
    luckynums.push_back(num);
    return;
  }
  bt(num * 10 + 4, idx + 1, n);
  bt(num * 10 + 7, idx + 1, n);
  return;
}
int upperbnd(int l, int r, int val) {
  int low = l, high = r, ans = r + 1;
  while (low <= high) {
    int mid = (low + high) / 2;
    if (mid > val) {
      ans = min(ans, mid);
      high = mid - 1;
    } else
      low = mid + 1;
  }
  return ans;
}
int lowerbnd(int l, int r, int val) {
  int low = l, high = r, ans = r + 1;
  while (low <= high) {
    int mid = (low + high) / 2;
    if (mid >= val) {
      ans = min(ans, mid);
      high = mid - 1;
    } else
      low = mid + 1;
  }
  return ans;
}
int main() {
  luckynums.push_back(0);
  for (int i = 1; i <= 9; i++) bt(0, 0, i);
  int l1, r1, l2, r2, k;
  scanf("%d%d%d%d%d", &l1, &r1, &l2, &r2, &k);
  long long poss = 0;
  luckynums.push_back(1e9 + 5);
  for (int i = 1, j = k; j < luckynums.size() - 1; i++, j++) {
    int yr = lowerbnd(l2, r2, luckynums[j + 1]);
    int yl = lowerbnd(l2, r2, luckynums[j]);
    yr--;
    int xl = upperbnd(l1, r1, luckynums[i - 1]);
    int xr = upperbnd(l1, r1, luckynums[i]);
    xr--;
    if (xl <= luckynums[i] && xr <= luckynums[i] && xl > luckynums[i - 1] &&
        yr < luckynums[j + 1] && yl < luckynums[j + 1] && yl >= luckynums[j] &&
        yr >= luckynums[j]) {
      int c1 = xr - xl + 1;
      int c2 = yr - yl + 1;
      poss += 1LL * c1 * c2;
    }
    int oldyl = yl, oldxr = xr;
    yr = lowerbnd(l1, r1, luckynums[j + 1]);
    yl = lowerbnd(l1, r1, luckynums[j]);
    yr--;
    xl = upperbnd(l2, r2, luckynums[i - 1]);
    xr = upperbnd(l2, r2, luckynums[i]);
    xr--;
    if (xl <= luckynums[i] && xr <= luckynums[i] && xl > luckynums[i - 1] &&
        yr < luckynums[j + 1] && yl < luckynums[j + 1] && yl >= luckynums[j] &&
        yr >= luckynums[j]) {
      int h = 0;
      if (yl == oldxr) {
        h += (oldyl - xl);
        yl++;
      }
      int c1 = xr - xl + 1;
      int c2 = yr - yl + 1;
      poss += 1LL * c1 * c2 + h;
    }
  }
  cout << setprecision(15) << fixed
       << (double)poss / (1LL * (r1 - l1 + 1) * (r2 - l2 + 1)) << endl;
}