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 num[2000], cnt;
void Gen(void) {
  cnt = 1;
  num[0] = 0;
  for (int len = 1; len <= 9; ++len) {
    for (int s = 0; s < 1 << len; ++s) {
      int x = 0;
      for (int i = 0; i < len; ++i) {
        x = 10 * x + ((s >> i & 1) ? 4 : 7);
      }
      num[cnt++] = x;
    }
  }
  num[cnt] = 2e9;
  sort(num, num + cnt);
}
struct Range {
  int l, r;
  Range(int _l = 0, int _r = 0) : l(_l), r(_r) {
    if (l > r) {
      l = 0;
      r = -1;
    }
  }
  Range operator&(const Range &b) const {
    return Range(max(l, b.l), min(r, b.r));
  }
  int Size(void) const { return r - l + 1; }
};
int main(void) {
  Gen();
  int pl, pr, vl, vr, k;
  scanf("%d%d%d%d%d", &pl, &pr, &vl, &vr, &k);
  Range p0(pl, pr), v0(vl, vr);
  long long ans = 0;
  for (int l = 1, r = k + 1; r <= cnt; ++l, ++r) {
    Range a(num[l - 1] + 1, num[l]), b(num[r - 1], num[r] - 1);
    Range p1 = p0 & a, v1 = v0 & b;
    Range p2 = p0 & b, v2 = v0 & a;
    Range p3 = p1 & p2, v3 = v1 & v2;
    ans += (long long)p3.Size() * (v1.Size() - v3.Size() + v2.Size());
    ans += (long long)(p1.Size() - p3.Size()) * v1.Size();
    ans += (long long)(p2.Size() - p3.Size()) * v2.Size();
  }
  double ans2 = (double)ans / ((long long)p0.Size() * v0.Size());
  printf("%.20lf\n", ans2);
  return 0;
}