2019.03.19_C

#include <bits/stdc++.h>

#define F first
#define S second
#define ll long long
#define ull unsigned long long
#define ld long double
#define SELO ""
#define openfiles ifstream cin("input"  SELO  ".txt"); ofstream cout("output"  SELO  ".txt");
#define faster ios_base::sync_with_stdio(NULL); cin.tie(0); cout.tie(0);
#define all(x) x.begin(), x.end()

using namespace std;

int main()
{
    openfiles
    string a;
    ll n;
    cin >> a >> n;
    vector <ld> dp2(n + 1), dp5(n + 1);
    ll sum = 0;
    ld cnt5 = 0, cnt2 = 0;
    for(int i = 0; i < a.size(); i++)
    {
        sum = (a[i] - '0' + sum) % 3;
        if((a[i] - '0') % 2 == 0)
            cnt2++;
        if(a[i] == '5')
            cnt5++;
    }
    if(a.back() == '5')
        dp5[0] = 1;
    if((a.back() - '0') % 2 == 0 && sum == 0)
        dp2[0] = 1;
    ld n1 = a.size();
    for(int i = 1; i <= n; i++)
    {
        dp5[i] = max(dp5[i - 1] * ((n1 - 2) / n1 + 2 / n1 * (cnt5 - 1) / (n1 - 1)) + (1 - dp5[i - 1]) * (2.0 / n1 * (cnt5) / (n1 - 1)), dp5[i]);
    }
    if(sum == 0)
        for(int i = 1; i <= n; i++)
        {
            dp2[i] = max(dp2[i - 1] * ((n1 - 2) / n1 + 2 / n1 * (cnt2 - 1) / (n1 - 1)) + (1 - dp2[i - 1]) * (2.0 / n1 * (cnt2) / (n1 - 1)), dp2[i]);
        }
    cout << fixed << setprecision(20) << dp2[n] + dp5[n];
}