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>
int const koll = 4000;
int beauty[koll], numb[20], col = 1;
int pl, pr, vl, vr, k;
long long kol;
int max(int a, int b) { return a > b ? a : b; }
int min(int a, int b) { return a > b ? b : a; }
bool beaty(int n) {
  while (n > 0) {
    if (n % 10 != 4 && n % 10 != 7) {
      return false;
    }
    n /= 10;
  }
  return true;
}
void makebeauty(int n, int k) {
  int i, pow10 = 1, num;
  if (k == n) {
    num = 0;
    numb[n] = 4;
    for (i = 0; i < n; i++) {
      num += numb[n - i] * pow10;
      pow10 *= 10;
    }
    beauty[col] = num;
    col++;
    num = 0;
    numb[n] = 7;
    pow10 = 1;
    for (i = 0; i < n; i++) {
      num += numb[n - i] * pow10;
      pow10 *= 10;
    }
    beauty[col] = num;
    col++;
    return;
  }
  numb[k] = 4;
  makebeauty(n, k + 1);
  numb[k] = 7;
  makebeauty(n, k + 1);
  return;
}
bool inp(int n) { return ((n >= pl) && (n <= pr)) ? true : false; }
bool inv(int n) { return ((n >= vl) && (n <= vr)) ? true : false; }
int main() {
  int i, j, n;
  scanf("%d %d %d %d %d", &pl, &pr, &vl, &vr, &k);
  for (j = 1; j < 10; j++) {
    makebeauty(j, 1);
  }
  beauty[col] = 1000 * 1000 * 1000 + 3;
  for (i = 1; i < col; i++) {
    if (i + k - 1 <= col) {
      if (inp(beauty[i])) {
        if (inv(beauty[i + k - 1])) {
          kol += (long long)(beauty[i] - max(beauty[i - 1] + 1, pl) + 1) *
                 (min(vr, beauty[i + k] - 1) - beauty[i + k - 1] + 1);
        } else {
          if ((vr > beauty[i + k - 1]) && (vl <= beauty[i + k])) {
            kol += (long long)(beauty[i] - max(beauty[i - 1] + 1, pl) + 1) *
                   (min(vr, beauty[i + k] - 1) - vl + 1);
          }
        }
      } else {
        if ((pr > beauty[i - 1]) && (pl < beauty[i])) {
          if (inv(beauty[i + k - 1])) {
            kol += (long long)(pr - max(beauty[i - 1] + 1, pl) + 1) *
                   (min(vr, beauty[i + k] - 1) - beauty[i + k - 1] + 1);
          } else {
            if ((vr > beauty[i + k - 1]) && (vl < beauty[i + k])) {
              kol += (long long)(pr - max(beauty[i - 1] + 1, pl) + 1) *
                     (min(vr, beauty[i + k] - 1) - vl + 1);
            }
          }
        }
      }
      if (inv(beauty[i])) {
        if (inp(beauty[i + k - 1])) {
          kol += (long long)(beauty[i] - max(beauty[i - 1] + 1, vl) + 1) *
                 (min(pr, beauty[i + k] - 1) - beauty[i + k - 1] + 1);
        } else {
          if ((pr > beauty[i + k - 1]) && (pl <= beauty[i + k])) {
            kol += (long long)(beauty[i] - max(beauty[i - 1] + 1, vl) + 1) *
                   (min(pr, beauty[i + k] - 1) - pl + 1);
          }
        }
      } else {
        if ((vr > beauty[i - 1]) && (vl < beauty[i])) {
          if (inp(beauty[i + k - 1])) {
            kol += (long long)(vr - max(beauty[i - 1] + 1, vl) + 1) *
                   (min(pr, beauty[i + k] - 1) - beauty[i + k - 1] + 1);
          } else {
            if ((pr > beauty[i + k - 1]) && (pl < beauty[i + k])) {
              return 0;
              kol += (long long)(vr - max(beauty[i - 1] + 1, vl) + 1) *
                     (min(pr, beauty[i + k] - 1) - pl + 1);
            }
          }
        }
      }
    }
  }
  int a = max(pl, vl), b = min(pr, vr);
  if (k == 1)
    for (i = 1; i < col; i++)
      if (beauty[i] >= a && beauty[i] <= b) kol--;
  printf("%.12lf\n",
         (1.0 * kol) / ((1.0 * (pr - pl + 1)) * (1.0 * (vr - vl + 1))));
  return 0;
}