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 program to find the value α=min\\{a_1, a_2, .
 def find(arr,m,n):
    maxArr = [0]*n
    
    for j in range(n):
        for i in range(m):
            if arr[i][j]>maxArr[j]:
                maxArr[j]=arr[i][j]
    r = min(maxArr)
    l = 0
    ans = 0
    while r>=l:
        mid = (r+l)//2
        for i in range(m):
            count = 0
            for j in range(n):
                if arr[i][j] >= mid:
                    count += 1
            if count>1:
                ans = mid
                l = mid + 1
                break
        if count<2:
            r = mid - 1
    
    return ans
        
        

    
res = []
r = int(input())
for i in range(r):
    input()
    [m, n] = list(map(int, input().split()))
    arr = []
    for i in range(m):
        arr.append(list(map(int, input().split())))
    res.append(find(arr, m, n))

for i in res:
    print(i)