#include <iostream>
#include <vector>
#include <algorithm>
#include <numeric>
#include <climits>
#include <cmath>

using namespace std;

// Function to compute the greatest common divisor (GCD)
int gcd(int a, int b) {
    while (b != 0) {
        int temp = b;
        b = a % b;
        a = temp;
    }
    return a;
}

// Function to generate all divisors of n greater than 1
vector<int> getDivisors(int n) {
    vector<int> divisors;
    for (int i = 2; i <= sqrt(n); ++i) {
        if (n % i == 0) {
            divisors.push_back(i);
            if (i != n / i) {
                divisors.push_back(n / i);
            }
        }
    }
    divisors.push_back(n);
    sort(divisors.begin(), divisors.end());
    return divisors;
}

void solve() {
    int t;
    cin >> t;
    while (t--) {
        int n, a1;
        cin >> n >> a1;
        vector<int> a(n - 1);
        for (int i = 0; i < n - 1; ++i) {
            cin >> a[i];
        }

        // Generate all possible k values (divisors of n)
        vector<int> divisors = getDivisors(n);

        // Initialize the minimum ratio to a large value
        int min_p = INT_MAX, min_q = 1;

        // Simulate each possible position for the captain
        for (int pos = 0; pos <= n; ++pos) {
            // Create the full skill array with a1 in the chosen position
            vector<int> full_a;
            for (int i = 0; i < pos; ++i) {
                full_a.push_back(a[i]);
            }
            full_a.push_back(a1);
            for (int i = pos; i < n - 1; ++i) {
                full_a.push_back(a[i]);
            }

            // For each divisor k
            for (int k : divisors) {
                // Calculate the sum of skills for each group
                vector<int> group_sums(k, 0);
                for (int i = 0; i < n; ++i) {
                    group_sums[i % k] += full_a[i];
                }

                // Find the maximum and minimum group sums
                int x_max = *max_element(group_sums.begin(), group_sums.end());
                int x_min = *min_element(group_sums.begin(), group_sums.end());

                // Calculate the ratio
                int p = x_max, q = x_min;
                int common_divisor = gcd(p, q);
                p /= common_divisor;
                q /= common_divisor;

                // Update the minimum ratio
                if ((long long)p * min_q < (long long)q * min_p) {
                    min_p = p;
                    min_q = q;
                }
            }
        }

        // Output the result
        cout << min_p << " " << min_q << endl;
    }
}

int main() {
    ios_base::sync_with_stdio(false);
    cin.tie(nullptr);
    solve();
    return 0;
}