Hi, I am a bit confused in the kind of logic used in the problem 991C Candies. The tutorial says that I have to produce a K using binary search every time and then check if for that k the person consumes more than half of the total candies. But I couldnt understand how the K is being generated using binary search. Basically can someone please explain me the logic in details?

Thank you!.

link to the problem: [http://codeforces.com/contest/991/problem/C] The model solution from tutorial is given below:

#include <bits/stdc++.h>
 
using namespace std;
 
bool check(long long k, long long n) {
    long long sum = 0;
    long long cur = n;
    while (cur > 0) {
        long long o = min(cur, k);
        sum += o;
        cur -= o;
        cur -= cur / 10;
    }
    return sum * 2 >= n;
}
 
int main() {
    long long n;
    cin >> n;
 
    long long l = 1, r = n;
    long long ans = r;
    while (l <= r) {
        long long k = (l + r) / 2;
        if (check(k, n)) {
            ans = k;
            r = k - 1;
        }
        else
            l = k + 1;     }
 
    cout << ans << endl;
}