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;
int main() {
  ios::sync_with_stdio(false);
  int Pl, Pr, Vl, Vr, K;
  { cin >> Pl >> Pr >> Vl >> Vr >> K; }
  vector<int> luckyNums;
  {
    for (int l = 1; l < 10; ++l) {
      for (int s = 0; s < 1 << l; ++s) {
        int64_t n = 0;
        for (int i = 0; i < l; ++i) n = n * 10 + (s >> i & 1 ? 7 : 4);
        if (n <= 1e9) luckyNums.push_back(n);
      }
    }
    sort(luckyNums.begin(), luckyNums.end());
  }
  auto coverRange = [](int l1, int r1, int l2, int r2) {
    if (r1 < l1 || r2 < l2) return make_pair(0, -1);
    if (l1 > l2) tie(l1, r1, l2, r2) = make_tuple(l2, r2, l1, r1);
    if (r1 < l2) return make_pair(0, -1);
    return make_pair(max(l1, l2), min(r1, r2));
  };
  auto rangeSize = [](pair<int, int> r) { return r.second - r.first + 1; };
  int64_t luckyCnt = 0;
  for (int i = 0; i + K <= luckyNums.size(); ++i) {
    int a = luckyNums[i];
    int b = luckyNums[i + K - 1];
    if (a < min(Vl, Pl) || max(Vr, Pr) < b) continue;
    int pa = i ? luckyNums[i - 1] + 1 : 0;
    int nb = i + K < luckyNums.size() ? luckyNums[i + K] - 1 : 1e9;
    luckyCnt += (int64_t)rangeSize(coverRange(Vl, Vr, pa, a)) *
                rangeSize(coverRange(Pl, Pr, b, nb));
    luckyCnt += (int64_t)rangeSize(coverRange(Pl, Pr, pa, a)) *
                rangeSize(coverRange(Vl, Vr, b, nb));
    int x, y;
    tie(x, y) = coverRange(pa, a, b, nb);
    tie(x, y) = coverRange(x, y, Pl, Pr);
    tie(x, y) = coverRange(x, y, Vl, Vr);
    luckyCnt -= rangeSize(make_pair(x, y));
  }
  long double res = (long double)luckyCnt / (Pr - Pl + 1) / (Vr - Vl + 1);
  cout << fixed << setprecision(10) << res << endl;
}