human
PYTHON3 solution for "Vlad has n friends, for each of whom he wants to buy one gift for the New Year.

There are m shops in the city, in each of which he can buy a gift for any of his friends. If the j-th friend (1 ≤ j ≤ n) receives a gift bought in the shop with the number i (1 ≤ i ≤ m), then the friend receives p_{ij} units of joy. The rectangular table p_{ij} is given in the input.

Vlad has time to visit at most n-1 shops (where n is the number of friends). He chooses which shops he will visit and for which friends he will buy gifts in each of them.

Let the j-th friend receive a_j units of joy from Vlad's gift. Let's find the value α=min\\{a_1, a_2, ..., a_n\}. Vlad's goal is to buy gifts so that the value of α is as large as possible. In other words, Vlad wants to maximize the minimum of the joys of his friends.

For example, let m = 2, n = 2. Let the joy from the gifts that we can buy in the first shop: p_{11} = 1, p_{12}=2, in the second shop: p_{21} = 3, p_{22}=4.

Then it is enough for Vlad to go only to the second shop and buy a gift for the first friend, bringing joy 3, and for the second — bringing joy 4. In this case, the value α will be equal to min\{3, 4\} = 3

Help Vlad choose gifts for his friends so that the value of α is as high as possible. Please note that each friend must receive one gift. Vlad can visit at most n-1 shops (where n is the number of friends). In the shop, he can buy any number of gifts.

Input

The first line of the input contains an integer t (1 ≤ t ≤ 10^4) — the number of test cases in the input.

An empty line is written before each test case. Then there is a line containing integers m and n (2 ≤ n, 2 ≤ n ⋅ m ≤ 10^5) separated by a space — the number of shops and the number of friends, where n ⋅ m is the product of n and m.

Then m lines follow, each containing n numbers. The number in the i-th row of the j-th column p_{ij} (1 ≤ p_{ij} ≤ 10^9) is the joy of the product intended for friend number j in shop number i.

It is guaranteed that the sum of the values n ⋅ m over all test cases in...":
assistant
#Here is Python code to find the value α=min\\{a_1, a_2, .
 def main():
    test = int(input())

    for idt in range(test):
        _ = input()
        m, n = map(int, input().split())
        store_person = [[0] * n for _ in range(m)]
        for i in range(m):
            a = list(map(int, input().split()))
            for j in range(n):
                store_person[i][j] = a[j]
        person_store = [[] for _ in range(n)]
        for i in range(n):
            for j in range(m):
                # person_store[i][j] = store_person[j][i]
                person_store[i].append([store_person[j][i], j, i])
            person_store[i].sort(reverse=True)
        # print(*person_store, sep="\n")
        selected = set()
        maxs = [0] * n 
        for i in range(n):
            score, store, person = person_store[i][0]
            maxs[person] = max(maxs[person], score)
            selected.add(store)
        if len(selected) <= n - 1:
            print(min(maxs))
            continue 
        
        ans = 0 
        for j in range(n):
            for k in range(j + 1, n):
                cur = float('inf')
                for i in range(n):
                    if i == j or i == k:
                        continue
                    cur = min(cur, maxs[i])
                opt = 0 
                for i in range(m):
                    opt = max(opt, min(store_person[i][j], store_person[i][k]))
                cur = min(cur, opt)
                ans = max(ans, cur)
        print(ans)
    
    return 

if __name__ == '__main__':
    main()