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 n, i, k;
long long pl, pr, vl, vr, minp, maxp, minv, maxv;
long long lucky[2000];
long long numerator, denumerator;
void generate_lucky(long long me) {
  lucky[++n] = me;
  if (me * 10 + 4 <= 1000000000) generate_lucky(10 * me + 4);
  if (me + 10 + 7 <= 1000000000) generate_lucky(10 * me + 7);
}
long long intersection(long long l1, long long r1, long long l2, long long r2) {
  return (max(0LL, min(r1, r2) - max(l1, l2) + 1));
}
int main(int argc, char const *argv[]) {
  scanf("%lld%lld%lld%lld%d", &pl, &pr, &vl, &vr, &k);
  generate_lucky(4), generate_lucky(7);
  sort(lucky + 1, lucky + n + 1);
  numerator = 0;
  denumerator = (pr - pl + 1) * (vr - vl + 1);
  for (i = 1; i <= n - k + 1; ++i) {
    if (lucky[i] < min(pl, vl) || lucky[i + k - 1] > max(pr, vr)) continue;
    minp = (i == 1 ? pl : lucky[i - 1] + 1);
    maxp = lucky[i];
    minv = lucky[i + k - 1];
    maxv = (i == n - k + 1 ? vr : lucky[i + k - 1 + 1] - 1);
    numerator +=
        intersection(minp, maxp, pl, pr) * intersection(minv, maxv, vl, vr);
    minv = (i == 1 ? vl : lucky[i - 1] + 1);
    maxv = lucky[i];
    minp = lucky[i + k - 1];
    maxp = (i == n - k + 1 ? pr : lucky[i + k - 1 + 1] - 1);
    numerator +=
        intersection(minp, maxp, pl, pr) * intersection(minv, maxv, vl, vr);
    if (k == 1 && lucky[i] >= pl && lucky[i] <= pr && lucky[i] >= vl &&
        lucky[i] <= vr)
      --numerator;
  }
  printf("%.15lf\n", (double)numerator / (double)denumerator);
  return 0;
}