Family reunion

#include <bits/stdc++.h>
using namespace std;
using lint = long long;
using pi = array<lint, 2>;
#define sz(a) ((int)(a).size())
#define all(a) (a).begin(), (a).end()
const int MAXN = 2000005;
const int MAXA = 26;
 
int binom(int u, int v) {
	int ans = 1;
	for (int i = 1; i <= v; i++)
		ans *= u + 1 - i, ans /= i;
	return ans;
}
int main() {
	ios_base::sync_with_stdio(0);
	cin.tie(0);
	cout.tie(0);
	int n, m, k;
	cin >> n >> m >> k;
	for (int i = 0; i < m; i++) {
		vector<int> ord(2 * k + 1);
		for (int j = 0; j < sz(ord); j++)
			cin >> ord[j], ord[j]--;
		ord.resize(7);
		for (int i = 7; i >= 4; i--) {
			vector<int> nord;
			int mx = *max_element(all(ord)) + 1;
			if (mx > 69) {
				for (int j = 0; j < sz(ord) - 1; j++) {
					int u = ord[j], v = ord[j + 1];
					int i = 0;
					while (((u ^ v) >> i) % 2 == 0)
						i++;
					nord.push_back(2 * i + (u >> i) % 2);
				}
			} else {
				int k = 2;
				while (binom(2 * k, k) < mx)
					k++;
				vector<int> cand;
				for (int i = 0; i < (1 << (2 * k)); i++) {
					if (__builtin_popcount(i) == k)
						cand.push_back(i);
				}
				for (int j = 0; j < sz(ord) - 1; j++) {
					int u = ord[j], v = ord[j + 1];
					u = cand[u], v = cand[v];
					int i = 0;
					while ((u >> i) % 2 == 1 || (v >> i) % 2 == 0)
						i++;
					nord.push_back(i);
				}
			}
			ord = nord;
		}
		if (ord[1] < 3)
			cout << (char)(ord[1] + 'A') << "\n";
		else {
			int u = 0;
			if (ord[0] == u || ord[2] == u)
				u++;
			if (ord[0] == u || ord[2] == u)
				u++;
			cout << (char)(u + 'A') << "\n";
		}
	}
}

Test 1

Group: 1

Verdict: UNKNOWN

Test 2

Group: 2

Verdict: UNKNOWN

Test 3

Group: 3

Verdict: UNKNOWN