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 double eps = 1e-8;
const int nm = 300005;
int n, k, m, t;
long long res;
int a[nm];
char s[nm];
bool check[nm];
int tmp[12], ntmp;
int Luck[1030], nL;
void Try(int vt, int sl) {
  if (vt > sl) {
    int x = 0, i;
    for (i = 1; i <= sl; i++) x = x * 10 + tmp[i];
    Luck[++nL] = x;
    return;
  }
  tmp[vt] = 4;
  Try(vt + 1, sl);
  tmp[vt] = 7;
  Try(vt + 1, sl);
}
int vl, vr, pl, pr;
long long Giao(int x1, int x2, int y1, int y2) {
  if (y1 < x1) swap(x1, y1), swap(x2, y2);
  if (y1 > x2) return 0ll;
  return (min(x2, y2) - max(x1, y1) + 1);
}
int main() {
  int i, j, x, y, z, w;
  for (i = 1; i <= 9; i++) Try(1, i);
  Luck[nL + 1] = MOD;
  scanf("%d%d%d%d", &vl, &vr, &pl, &pr);
  scanf("%d", &k);
  for (i = 1; i <= 1024 - k; i++) {
    j = i + k;
    res += Giao(Luck[i - 1] + 1, Luck[i], vl, vr) *
           Giao(Luck[j - 1], Luck[j] - 1, pl, pr);
    res += Giao(Luck[i - 1] + 1, Luck[i], pl, pr) *
           Giao(Luck[j - 1], Luck[j] - 1, vl, vr);
    if (k == 1 && Luck[i] >= vl && Luck[i] <= vr && Luck[i] >= pl &&
        Luck[i] <= pr)
      res--;
  }
  printf("%.12lf ", (double)res / (vr - vl + 1) / (pr - pl + 1));
  ;
  return 0;
}