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;
using ll = long long int;
using ld = long double;
using pi = pair<int, int>;
const double PI = acos(-1.0);
const double eps = 1e-9;
const ll mod = 1e9 + 7;
const int inf = 1e7;
const int MAXN = 1e5 + 5;
vector<ll> lucky;
void gen(ll num) {
  if (num > 2e9) return;
  if (num > 0) lucky.push_back(num);
  gen(num * 10 + 4);
  gen(num * 10 + 7);
}
void cp() {
  ll pL, pR, vL, vR;
  int k;
  cin >> pL >> pR >> vL >> vR >> k;
  gen(0);
  sort(lucky.begin(), lucky.end());
  ll total = 0;
  for (int i = 0; i + k - 1 < ((int)lucky.size()); i++) {
    bool over = true;
    ll L = pL;
    if (i) L = max(L, lucky[i - 1] + 1);
    ll R = min(pR, lucky[i]);
    over &= R == lucky[i];
    ll dL = max(0LL, R - L + 1);
    L = max(vL, lucky[i + k - 1]);
    R = vR;
    if (i + k < ((int)lucky.size())) R = min(R, lucky[i + k] - 1);
    over &= L == lucky[i];
    ll dR = max(0LL, R - L + 1);
    total += dL * dR;
    L = vL;
    if (i) L = max(L, lucky[i - 1] + 1);
    R = min(vR, lucky[i]);
    over &= R == lucky[i];
    dL = max(0LL, R - L + 1);
    L = max(pL, lucky[i + k - 1]);
    R = pR;
    if (i + k < ((int)lucky.size())) R = min(R, lucky[i + k] - 1);
    over &= L == lucky[i];
    dR = max(0LL, R - L + 1);
    total += dL * dR - over;
  }
  ld ans = ld(total) / ld(pR - pL + 1) / ld(vR - vL + 1);
  cout << setprecision(20) << fixed;
  ;
  cout << ans << '\n';
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  ;
  int t;
  t = 1;
  while (t--) {
    cp();
  }
  return 0;
}