1177B-Digit_Sequence(Hard_Edition).cpp

/*
    written by Pankaj Kumar.
    country:-INDIA
    Institute: National Institute of Technology, Uttarakhand
*/
#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
using namespace std;
using namespace __gnu_pbds;
typedef long long ll ;
typedef vector<ll> vl;
typedef vector<vector<ll>> vvl;
#define speed cin.tie(0);cout.tie(0);ios_base::sync_with_stdio(0);
/*  Abbrevations  */
#define ff first
#define ss second
#define mp make_pair
#define line cout<<endl;
#define pb push_back
// loops
#define forin(arr,n) for(ll i=0;i<n;i++) cin>>arr[i];
// Some print
#define no cout<<"NO"<<endl;
#define yes cout<<"YES"<<endl;
// sort
#define all(V) (V).begin(),(V).end()
#define srt(V) sort(all(V))
#define srtGreat(V) sort(all(V),greater<ll>())
// some extra
#define printv(v) for(ll i=0;i<ll(v.size());i++){cout<<v[i]<<" ";} line;
#define precision(x) cout<<fixed<<setprecision(x);
#define sz(V) ll(V.size())
// datatype definination
#define ordered_set tree<ll,null_type,less<ll>,rb_tree_tag,tree_order_statistics_node_update>


ll ppow(ll n, ll m, ll mod){
    if(m==0) return 1;
    ll tmp=ppow(n, m/2, mod);
    tmp=tmp*tmp%mod;
    return m%2 ? tmp*n%mod: tmp;
}
namespace mod_operations{
    ll modInv(ll n, ll mod){
        return ppow(n,mod-2, mod);
    }
    ll modAdd(ll n, ll m, ll mod){
        n=(n%mod+mod)%mod; m=(m%mod+mod)%mod;
        return (n+m)%mod;
    }
    ll modMul(ll n, ll m, ll mod){
        n=(n%mod+mod)%mod; m=(m%mod+mod)%mod;
        return n*m %mod;
    }
    ll modSub(ll n, ll m, ll mod){
        n=(n%mod+mod)%mod; m=(m%mod+mod)%mod;
        return modAdd(n,-m, mod);
    }
    ll modDiv(ll n, ll m, ll mod){
        return modMul(n, modInv(m, mod), mod);
    }
}
using namespace mod_operations;


class Codeforces
{
    private:
        // read only variable
        const ll INF=1e18;
        const ll mod1=1e9+7;
        const ll mod2=998244353;
        vl v;


    public:
        Codeforces(){
            v.resize(17);
        }

        ll power(ll x,ll y){
            ll result=1;
            while(y>0){
                if(y&1){
                    result*=x;
                }
                y>>=1;
                x*=x;
            }
            return result;
        }

        ll power(ll x,ll y,ll mod){
            ll result=1;
            x%=mod;
            while(y>0){
                if(y&1){
                    result*=x;
                    result%=mod;
                }
                y>>=1;
                x*=x;
                x%=mod;
            }
            return result;
        }

        ll str_to_num(string s)
        {
            stringstream pk(s);
            ll num;
            pk>>num;
            return num;
        }

        string num_to_str(ll num)
        {
            return to_string(num);
        }
        // Techniques :
        // divide into cases, brute force, pattern finding
        // sort, greedy, binary search, two pointer
        // transform into graph

        // Experience :
        // Cp is nothing but only observation and mathematics.
        void cal(vector<ll>& v){
            for(ll i=1;i<=16;i++){
                this->v[i]=((9*i*pow(10,i-1)));
            }
            return ;
        }

        ll solve()
        {
            cal(this->v);
            // printv(this->v);
            ll query=1;
            // cin>>query;
            while(query--){
                ll k;
                cin>>k;
                ll sum=0;
                ll length_of_number=0;
                for(ll i=0;i<17;i++){
                    sum+=this->v[i];
                    if(sum<=k){
                        length_of_number=i+1;
                    }
                    else{
                        break;
                    }
                }
                sum-=this->v[length_of_number];
                // cout<<"sum : "<<sum<<endl;
                ll difference=k-sum;
                // cout<<"difference : "<<difference<<endl;
                ll starting_number=pow(10,length_of_number-1);
                ll distance_from_starting_number=(difference/length_of_number);
                sum+=(distance_from_starting_number*length_of_number);
                ll actual_number=starting_number+distance_from_starting_number-1;
                ll remainder=difference%length_of_number;
                // cout<<"remainder : "<<remainder<<endl;
                // cout<<"actual_number : "<<actual_number<<endl;
                // cout<<"sum : "<<sum<<endl;
                if(remainder==0){
                    cout<<actual_number%10<<endl;
                }
                else{
                    actual_number++;
                    string final_number_as_string=to_string(actual_number);
                    // cout<<"final actual number : "<<actual_number<<endl;
                    cout<<final_number_as_string[remainder-1]<<endl;
                }
            }
                

            return 0;
        }
};


/*  --------------------MAIN PROGRAM----------------------------*/

int main()
{
    speed;
    /* #ifndef ONLINE_JUDGE
        freopen("input.txt","r",stdin);
        freopen("output.txt","w",stdout);
    #endif */
    ll TestCase=1;
    // cin>>TestCase;
    while(TestCase--)
    {
        Codeforces cf;
        cf.solve();
    }
}
/* -----------------END OF PROGRAM --------------------*/
/*
* stuff you should look before submission
* constraint and time limit
* int overflow
* special test case (n=0||n=1||n=2)
* don't get stuck on one approach if you get wrong answer
*/