Codeforces Round 762 (Div. 3) |
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Finished |
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 ($$$1 \le j \le n$$$) receives a gift bought in the shop with the number $$$i$$$ ($$$1 \le i \le m$$$), 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 $$$\alpha=\min\{a_1, a_2, \dots, a_n\}$$$. Vlad's goal is to buy gifts so that the value of $$$\alpha$$$ 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 $$$\alpha$$$ will be equal to $$$\min\{3, 4\} = 3$$$
Help Vlad choose gifts for his friends so that the value of $$$\alpha$$$ 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.
The first line of the input contains an integer $$$t$$$ ($$$1 \le t \le 10^4$$$) — 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 $$$n$$$ ($$$2 \le n$$$, $$$2 \le n \cdot m \le 10^5$$$) separated by a space — the number of shops and the number of friends, where $$$n \cdot m$$$ 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 $$$p_{ij}$$$ ($$$1 \le p_{ij} \le 10^9$$$) is the joy of the product intended for friend number $$$j$$$ in shop number $$$i$$$.
It is guaranteed that the sum of the values $$$n \cdot m$$$ over all test cases in the test does not exceed $$$10^5$$$.
Print $$$t$$$ lines, each line must contain the answer to the corresponding test case — the maximum possible value of $$$\alpha$$$, where $$$\alpha$$$ is the minimum of the joys from a gift for all of Vlad's friends.
5 2 2 1 2 3 4 4 3 1 3 1 3 1 1 1 2 2 1 1 3 2 3 5 3 4 2 5 1 4 2 7 9 8 1 9 6 10 8 2 4 6 5 2 1 7 9 7 2
3 2 4 8 2
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