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;
long double resnum, resden;
int e = 1;
long long A[5000], Deg[20];
int main() {
  int k, i, j, l;
  long long c, pl, pr, vl, vr;
  scanf("%I64d%I64d%I64d%I64d%d", &pl, &pr, &vl, &vr, &k);
  Deg[0] = 1ll, k--;
  for (i = 1; i <= 9; i++) {
    Deg[i] = Deg[i - 1] * 10ll;
    for (j = 0; j < (1 << i); j++) {
      c = 0;
      for (l = 0; l < i; l++) {
        if (j & (1 << l))
          c += 4ll * Deg[l];
        else
          c += 7ll * Deg[l];
      }
      A[e] = c, e++;
    }
  }
  sort(A, A + e);
  A[e] = 1234567890ll;
  for (i = 0; i + k < e; i++) {
    if (vl <= A[i] && pr >= A[i + k] && vr > A[i - 1] && pl < A[i + k + 1]) {
      resnum += (long double)((min(A[i], vr) - max(A[i - 1] + 1ll, vl) + 1ll) *
                              (min(A[i + k + 1] - 1ll, pr) - max(A[i + k], pl) +
                               1ll));
    }
    if (pl <= A[i] && vr >= A[i + k] && pr > A[i - 1] && vl < A[i + k + 1]) {
      resnum += (long double)((min(A[i], pr) - max(A[i - 1] + 1ll, pl) + 1ll) *
                              (min(A[i + k + 1] - 1ll, vr) - max(A[i + k], vl) +
                               1ll));
    }
    if (k == 0 && A[i] >= vl && A[i] <= vr && A[i] >= pl && A[i] <= pr)
      resnum -= (long double)(1.0);
  }
  resden = (long double)((pr - pl + 1ll) * (vr - vl + 1ll));
  printf("%.10lf\n", (double)(resnum / resden));
  return 0;
}