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.
 Give me a Python program to find the value α=min\\{a_1, a_2,?
assistant
#Here is Python program to find the value α=min\\{a_1, a_2, .

import sys, collections, math, bisect, heapq, random, functools,io,os,copy
input = sys.stdin.readline
out = sys.stdout.flush
def rep():
    a = list(map(int,input().split()))
    return a

def sep():
    a = list(input().split())
    return a

class UnionFind:
    def __init__(self, x) -> None:
        self.uf = [-1] * x

    def find(self, x):
        r = x
        while self.uf[x] >= 0:
            x = self.uf[x]

        while r != x:
            self.uf[r], r = x, self.uf[r]
        return x

    def union(self, x, y):
        ux, uy = self.find(x), self.find(y)
        if ux == uy:
            return
        if self.uf[ux] >= self.uf[uy]:
            self.uf[uy] += self.uf[ux]
            self.uf[ux] = uy
        else:
            self.uf[ux] += self.uf[uy]
            self.uf[uy] = ux
        return

    def __print__(self):
        return self.uf

def spfa(x,g,n):
    dis = [float('inf') for i in range(n)]
    dis[x] = 0
    state = [False for i in range(n)]
    state[x] = True
    queue = collections.deque()
    queue.append(x)
    while queue:
        cur = queue.popleft()
        state[cur] = False
        for next_ in g[cur]:
            if dis[next_] > dis[cur] + 1:
                dis[next_] = dis[cur] + 1
                if state[next_] == False:
                    state[next_] = True
                    queue.append(next_)
    return dis

def gcd(x,y):
    if y == 0:
        return x
    return gcd(y,x % y)

def valid(x,mat):
    m,n = len(mat),len(mat[0])
    cnt = [0 for i in range(m)]
    flag = [0 for i in range(n)]
    for i in range(m):
        for j in range(n):
            if mat[i][j] >= x:
                cnt[i] += 1
                flag[j] = 1
    return True if max(cnt) > 1 and sum(flag) == n else 0


def solve():
    t = input()
    m,n = map(int,input().split())
    matrix = [list(map(int,input().split())) for i in range(m)]
    l,r = float('inf'),float('inf')

    for j in range(n):
        temp = -float('inf')
        for i in range(m):
            temp =...