A13249 | Minimax Problem

You are given $n$ arrays $a_1$ , $a_2$ , ..., $a_n$ ; each array consists of exactly $m$ integers. We denote the $y$ -th element of the $x$ -th array as $a_{x, y}$ .

You have to choose two arrays $a_i$ and $a_j$ ( $1 \le i, j \le n$ , it is possible that $i = j$ ). After that, you will obtain a new array $b$ consisting of $m$ integers, such that for every $k \in [1, m]$ $b_k = \max(a_{i, k}, a_{j, k})$ .

Your goal is to choose $i$ and $j$ so that the value of $\min \limits_{k = 1}^{m} b_k$ is maximum possible.

The first line contains two integers $n$ and $m$ ( $1 \le n \le 3 \cdot 10^5$ , $1 \le m \le 8$ ) — the number of arrays and the number of elements in each array, respectively.

Then $n$ lines follow, the $x$ -th line contains the array $a_x$ represented by $m$ integers $a_{x, 1}$ , $a_{x, 2}$ , ..., $a_{x, m}$ ( $0 \le a_{x, y} \le 10^9$ ).

Print two integers $i$ and $j$ ( $1 \le i, j \le n$ , it is possible that $i = j$ ) — the indices of the two arrays you have to choose so that the value of $\min \limits_{k = 1}^{m} b_k$ is maximum possible. If there are multiple answers, print any of them.