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;
string BiggerLuckyNum(long long number) {
  string ans, num = to_string(number);
  int pos4 = -1;
  for (int i = 0; i < num.size(); ++i) {
    if (num[i] == '4') {
      ans.append("4");
      pos4 = i;
    }
    if (num[i] == '7') ans.append("7");
    if (num[i] < '4' || num[i] == '5' || num[i] == '6') {
      if (num[i] < '4') ans.append("4");
      if (num[i] == '5' || num[i] == '6') ans.append("7");
      ++i;
      for (; i < num.size(); ++i) ans.append("4");
      return ans;
    }
    if (num[i] > '7') {
      if (pos4 == -1) {
        ans.clear();
        for (int i = 0; i < num.size() + 1; ++i) ans.append("4");
        return ans;
      } else {
        ans[pos4] = '7';
        for (; i < num.size(); ++i) ans.append(" ");
        for (i = pos4 + 1; i < num.size(); ++i) ans[i] = '4';
        return ans;
      }
    }
  }
  return ans;
}
string SmallerLuckyNum(long long number) {
  string ans, num = to_string(number);
  int pos7 = -1;
  for (int i = 0; i < num.size(); ++i) {
    if (num[i] == '4') ans.append("4");
    if (num[i] == '7') {
      ans.append("7");
      pos7 = i;
    }
    if (num[i] > '7' || num[i] == '5' || num[i] == '6') {
      if (num[i] > '7') ans.append("7");
      if (num[i] == '5' || num[i] == '6') ans.append("4");
      ++i;
      for (i; i < num.size(); ++i) ans.append("7");
      return ans;
    }
    if (num[i] < '4') {
      if (pos7 == -1) {
        ans.clear();
        for (int i = 0; i < num.size() - 1; ++i) ans.append("7");
        if (ans == "") return "0";
        return ans;
      } else {
        ans[pos7] = '4';
        for (i; i < num.size(); ++i) ans.append(" ");
        for (i = pos7 + 1; i < num.size(); ++i) ans[i] = '7';
        return ans;
      }
    }
  }
  return ans;
}
long long Min(long long a, long long b) {
  if (b < 0 || a < 0) return 0;
  if (a < b) return a;
  return b;
}
double Probi(long long pl, long long pr, long long vl, long long vr, long k) {
  long long min = pl;
  if (min > pr) min = pr;
  if (min > vl) min = vl;
  if (min > vr) min = vr;
  long long max = pl;
  if (max < pr) max = pr;
  if (max < vl) max = vl;
  if (max < vr) max = vr;
  vector<long long> luckyNum;
  map<double, double> a, b;
  long long i = min - 1;
  if (min == 0) i = 0;
  double pro = 0;
  while (i <= max) {
    i = stoull(BiggerLuckyNum(i + 1));
    if (i <= max) luckyNum.push_back(i);
  }
  for (int i = 0; i < luckyNum.size(); ++i) {
    long long m = luckyNum[i];
    if (m < pl) {
      a[m] = 0;
      if (i == luckyNum.size() - 1)
        a[-m] = pr - pl + 1;
      else
        a[-m] = Min(pr - pl + 1, luckyNum[i + 1] - pl);
    }
    if (m < vl) {
      b[m] = 0;
      if (i == luckyNum.size() - 1)
        b[-m] = vr - vl + 1;
      else
        b[-m] = Min(vr - vl + 1, luckyNum[i + 1] - vl);
    }
    if (m > pr) {
      a[-m] = 0;
      if (i == 0)
        a[m] = pr - pl + 1;
      else
        a[m] = Min(pr - pl + 1, pr - luckyNum[i - 1]);
    }
    if (m > vr) {
      b[-m] = 0;
      if (i == 0)
        b[m] = vr - vl + 1;
      else
        b[m] = Min(vr - vl + 1, vr - luckyNum[i - 1]);
    }
    if (m >= pl && m <= pr) {
      if (i == 0)
        a[m] = m - pl + 1;
      else
        a[m] = Min(m - pl + 1, luckyNum[i] - luckyNum[i - 1]);
      if (i == luckyNum.size() - 1)
        a[-m] = pr - luckyNum[i] + 1;
      else
        a[-m] = Min(pr - m + 1, luckyNum[i + 1] - luckyNum[i]);
    }
    if (m >= vl && m <= vr) {
      if (i == 0)
        b[m] = m - vl + 1;
      else
        b[m] = Min(m - vl + 1, luckyNum[i] - luckyNum[i - 1]);
      if (i == luckyNum.size() - 1)
        b[-m] = vr - m + 1;
      else
        b[-m] = Min(vr - m + 1, luckyNum[i + 1] - luckyNum[i]);
    }
  }
  for (long long i = k - 1; i < luckyNum.size(); ++i) {
    long long x = luckyNum[i - k + 1];
    long long y = luckyNum[i];
    pro += a[x] * b[-y];
    pro += a[-y] * b[x];
    if (k == 1 && x >= pl && x <= pr && x >= vl && x <= vr && y >= pl &&
        y <= pr && y >= vl && y <= vr)
      --pro;
  }
  if (pro >= 0)
    return pro;
  else
    return 0;
}
int main(int argc, const char* argv[]) {
  long long pl, pr, vl, vr, k;
  cin >> pl >> pr >> vl >> vr >> k;
  double m = (pr - pl + 1) * (vr - vl + 1);
  double ans = Probi(pl, pr, vl, vr, k) / m;
  if (ans >= 1) ans = 1;
  cout << fixed << setprecision(12) << ans << endl;
  return 0;
}