F. The Head Revenge (hard version)

#include <bits/stdc++.h>
using namespace std;

#define cin(vec) for(auto& i : vec) cin >> i
#define cin_2d(vec, n, m) for(int i = 0; i < n; i++) for(int j = 0; j < m && cin >> vec[i][j]; j++);
#define cout(vec) for(auto& i : vec) cout << i << " "; cout << "\n";
#define cout_2d(vec, n, m) for(int i = 0; i < n; i++, cout << "\n") for(int j = 0; j < m && cout << vec[i][j] << " "; j++);
#define cout_map(mp) for(auto& [f, s] : mp) cout << f << "  " << s << "\n";
#define Time cerr << "Time Taken: " << (float)clock() / CLOCKS_PER_SEC << " Secs" << "\n";
#define fixed(n) fixed << setprecision(n)
#define ceil(n, m) (((n) / (m)) + ((n) % (m) ? 1 : 0))
#define fill(vec, value) memset(vec, value, sizeof(vec));
#define Num_of_Digits(n) ((int)log10(n)+1)
#define mod_combine(a, b, m) (((a % m) * (b % m)) % m)
#define all(vec) vec.begin(),vec.end()
#define rall(vec) vec.rbegin(),vec.rend()
#define sz(x) int(x.size())
#define fi first
#define se second
#define Pair pair < int, int >
#define ll long long
#define ull unsigned long long
#define Mod  1'000'000'007
#define OO 2'000'000'000
#define EPS 1e-9
#define PI acos(-1)

void AhMeD_HoSSaM(){
  ios_base::sync_with_stdio(false), cin.tie(nullptr), cout.tie(nullptr);
  #ifndef ONLINE_JUDGE
    freopen("input.txt", "r", stdin), freopen("output.txt", "w", stdout);
  #endif
}

void solve(){
    ll n;
    cin >> n;
    vector < ll > ranges = {0};
    // to make the array 1-based
    for(ll i = 1, range = 0; range <= n; i++){
        range = i * (9ll * pow(10ll, i - 1));
        ranges.push_back(range);
        // from 1 to 9 = 9,  from 10 to 99 = 90, from 100 to 999 = 900, .. and so on
    }
    for(int i = 1; i < sz(ranges); i++){
        // if n bigger than the range of the number of digit i remove them from n
        if(n > ranges[i]) n -= ranges[i];
        else {
            ll move = n / i, remain = n % i;
            // we want to know how many number to skip that they conatins number of digit i
            // and we must handle case that n divisable by i
            string curr = to_string((ll) pow(10, i - 1) + (remain == 0 ? move - 1 : move));
            cout << (remain == 0 ? curr.back() : curr[remain - 1]) << "\n";
            return;
        }
    }
}

int main(){
    AhMeD_HoSSaM();
    int t = 1;
    //cin >> t;
    while(t--)
        solve();
    Time
    return 0;
}