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, .
 from math import inf, gcd, log, log2, floor, ceil, sqrt
from collections import Counter, defaultdict
#from sortedcontainers import SortedList
DIRS = [[1,0], [0,1],[0,-1],[-1,0]]
MOD = 10**9+7
def solve(A):
    m, n = len(A), len(A[0])
    def is_good(mini):
        has_pair = False
        column = [0 for x in range(n)]
        for i in range(m):
            row_cnt = 0
            for j in range(n):
                row_cnt += A[i][j] >= mini
                column[j] |= A[i][j] >= mini
            has_pair |= row_cnt >= 2
        return has_pair & (sum(column) == n)

    l, r = 0, 10**9
    while l < r:
        mid = l + (r-l+1)//2
        if is_good(mid):
            l = mid
        else:
            r = mid-1

    return l

t = int(input())
for _ in range(t):
    input()
    A = []
    m, n = [int(x) for x in input().split(' ')]
    for _ in range(m):
        A.append([int(x) for x in input().split(' ')])
    print(solve(A))