human
Can you provide a Python code to find the value α=min\\{a_1, a_2, given the following:
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 check(x,mat,n,m):
    flag=False
    # we want n-1 go to shop so one shop have buy two gift
    # this flag for this
    pair=[False]*m
    for i in range(n):
        c=0
        for j in range(m):
            # print(i,j)
            if mat[i][j]>=x:
                pair[j]=True
                c+=1
        if c>1:
            flag=True
    if (not flag) and m>1:
        return False
 
    ans=sum(pair)
    if ans==m:
        return True
 
    return False
 
    
import sys
 
 
 
def solve():
    for t in range(1):
        s=input()
        n,m=map(int,input().split())
        
        arr=[]
        mx=sys.maxsize*-1
        for i in range(n):
            a=list(map(int,input().split()))
            mx=max(mx,max(a))
            arr.append(a)
        start=1
        end=mx
        ans=None
        while start<=end:
            mid=(start+end)//2
            if check(mid,arr,n,m):
                # print("ok",mid)
                ans=mid
                start=mid+1
            else:
                end=mid-1
        print(ans)
            
        
        
for _ in range(int(input())):
    solve()