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;
const int mod = 1000000007;
const int inf = 50000000;
const int maxn = 100010;
const long long lim = 5000000001;
vector<long long> lucky;
int pl, pr, vl, vr;
void generate(long long cur) {
  lucky.push_back(cur);
  long long nxt = cur;
  nxt = nxt * 10 + 4;
  if (nxt < lim) generate(nxt);
  nxt = cur;
  nxt = nxt * 10 + 7;
  if (nxt < lim) generate(nxt);
}
long long find_common(long long x1, long long y1, long long x2, long long y2) {
  long long x, y;
  y = min(y1, y2);
  x = max(x1, x2);
  return max(0ll, y - x + 1);
}
int main() {
  generate(0);
  sort(lucky.begin(), lucky.end());
  int i, k;
  double ans, x, y, p1, p2, cnt1, cnt2;
  ans = 0;
  scanf("%d%d%d%d%d", &pl, &pr, &vl, &vr, &k);
  p1 = (double)1.0 / (pr - pl + 1);
  p2 = (double)1.0 / (vr - vl + 1);
  for (i = 1; i + k <= lucky.size(); i++) {
    if (lucky[i + k - 1] > pr && lucky[i + k - 1] > vr) break;
    cnt1 = find_common(pl, pr, lucky[i - 1] + 1, lucky[i]);
    cnt2 = find_common(vl, vr, lucky[i + k - 1], lucky[i + k] - 1);
    x = (double)cnt1 * p1;
    y = (double)cnt2 * p2;
    ans = (ans + (x * y));
    cnt1 = find_common(pl, pr, lucky[i + k - 1], lucky[i + k] - 1);
    cnt2 = find_common(vl, vr, lucky[i - 1] + 1, lucky[i]);
    x = (double)cnt1 * p1;
    y = (double)cnt2 * p2;
    ans = (ans + (x * y));
    if (k == 1) {
      cnt1 = find_common(pl, pr, lucky[i], lucky[i]);
      cnt2 = find_common(vl, vr, lucky[i], lucky[i]);
      x = (double)cnt1 * p1;
      y = (double)cnt2 * p2;
      ans = (ans - (x * y));
    }
  }
  printf("%.12lf\n", ans);
  return 0;
}