Hello everyone,

I’m currently stuck on a Codeforces problem — Problem 2137B. While reading the official editorial, I got confused about one particular transformation step:

Each element is replaced by n + 1 - p[i].

I understand the use of n + 1, since we’re working with adjacent elements and need a length of n + 1. However, I don’t quite understand why we subtract p[i].

Also, I noticed that the editorial mentions a condition like: G C D ( p i + q i , p i + 1 + q i + 1 ) ≥ 3

I’m wondering if this relates to the property gcd(a, b) = gcd(a - b, b) where (a > b). Is that property being applied here?

And finally, does the condition hold simply because (n > 3) (since (n + 1 > 3)) — or is there a deeper reason behind it?

// C++ Version of the logic
#include <bits/stdc++.h>
using namespace std;

#define endl '\n'

int main() {
    ios::sync_with_stdio(false);
    cin.tie(nullptr);

    int t; cin >> t;
    while (t--) {
        int n; cin >> n;
        vector<int> a(n), b(n);
        for (int i = 0; i < n; i++) cin >> a[i];
        for (int i = 0; i < n; i++) b[i] = n - a[i] + 1; // ??
        for (int i = 0; i < n; i++) cout << b[i] << " ";
        cout << endl;
    }

    return 0;
}

I’d really appreciate it if someone could explain this step more clearly. I’m still a beginner, so a simple explanation would be very helpful.

Thank you in advance!