Peli

#include <bits/stdc++.h>

using namespace std;


void solve() {
    set<pair<int, int>> s;
    s.insert({1, 2});
    set<int> were;
    were.insert(1);
    were.insert(2);

    set<pair<int, int>> diag;
    diag.insert({0, 1});
    diag.insert({0, 0});

    for (int i = 1; i <= 2000; i++) {
        for (int j = 1; j <= 2000; j++) {
            if (!were.count(i) && !were.count(j) && !diag.count({0, abs(i - j)})) {
                s.insert({i, j});
                were.insert(i);
                were.insert(j);
                diag.insert({0, abs(i - j)});
            }
        }
    }

    int qt;
    cin >> qt;
    while (qt--) {
        int a, b;
        cin >> a >> b;
        if (s.count({a, b})) {
            cout << "second\n";
            continue;
        }
        swap(a, b);
        if (s.count({a, b})) {
            cout << "second\n";
        } else {
            cout << "first\n";
        }
    }
}

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

Test 1 (public)

Group: 1, 2, 3

Verdict: ACCEPTED

Test 2

Group: 1, 2, 3

Verdict: ACCEPTED

Test 3

Group: 2, 3

Verdict: ACCEPTED

Test 4

Group: 3

Verdict: ACCEPTED

Test 5

Group: 2, 3

Verdict: ACCEPTED

Test 6

Group: 3

Verdict: ACCEPTED