human
Write me a Python code to find the value α=min\\{a_1, a_2, given the following:
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...
from
assistant
#Here is Python code to find the value α=min\\{a_1, a_2, .
collections import defaultdict

# def return_min_in_2d(mat):

#     temp = None
#     min_val = float('inf')

#     for i in range(len(mat)):
        
#         if mat[i][0]
        

def get_sol(d_fr, shops):

    for key in d_fr:
        d_fr[key].sort(reverse=True)

    # # print("FRierds")
    # # print(d_fr)

    shops_ideal = []

    min_ideal = float('inf')
    for key in d_fr:
        shops_ideal.append(d_fr[key][0][1])
        min_ideal = min(min_ideal, d_fr[key][0][0])

    shop_d = {i: True for i in shops_ideal}
    
    # # print(shop_d, "ideal case", min_ideal, "friends", d_fr, len(d_fr), "len of shops", len(shops_ideal))

    if len(shop_d) <= len(d_fr.keys()) - 1:
        return min_ideal

    else:
        # print("DIrty case")
        # dirty case
        # now have to choose one shop for replacement

        val = 0

        for s_i in range(len(shops)):
            shops[s_i].sort(reverse=True)
            
            if s_i in shop_d:
                # taken in ideal case
                # oth position is taken
                # trying with 1st position
                temp = min(min_ideal, shops[s_i][1])

                val = max(val, temp)
            else:
                # it is not taken in an ideal case
                # both 0th and 1st positions are open
                temp = min(min_ideal, min(shops[s_i][: 2]))

                val = max(val, temp)

        return val
            

if __name__ == '__main__':

    for t in range(int(input())):

        blank = input()
        
        m, n = map(int, input().split())

        d_fr = defaultdict(lambda: [])
        shops = []

        for s_i in range(m):

            values = list(map(int, input().split()))
            shops.append(values)

            for f_i in range(len(values)):
                d_fr[f_i].append([values[f_i], s_i])

        
        
        print(get_sol(d_fr, shops))