human
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...
The above is tricky. Write me a correct solution in PYTHON3.
assistant
#Here is Python code to find the value α=min\\{a_1, a_2, .

import io,os
input = io.BytesIO(os.read(0, os.fstat(0).st_size)).readline

def main(t):

    s = input()
    m,n = map(int,input().split())
    friends = [[] for _ in range(n)]

    for i in range(m):
        temp = list( map(int,input().split()) )

        for j in range(n):
            friends[j].append( temp[j] )

    maximum = max(friends[0])
    for j in range(1,n):  maximum = min(maximum,max(friends[j]))

#    print(friends)

#    print(maximum)


    def judge(target):
        dic = {}
        for j in range(n):
            for i in range(m):
                if friends[j][i]>=target: 
                    if i in dic:  return True
                    dic[i] = 1

        return False

    front = 0
    rear = maximum+1

    while front<rear:
        mid = (front+rear)//2
        flag = judge(mid)
        if flag:
            front = mid + 1
        else:
            rear = mid 
    ans = front-1

    
 

    



        
        


    print(ans)
         
    
        
        



















T = int(input())
t = 1
while t<=T:
    main(t)
    t += 1