GCD Sum

You are given $n$ sequences $a_1, a_2, \dots, a_n$. Each of these sequences contains $m$ integers; let's denote the $j$-th element of the $i$-th sequence by $a_{i,j}$. Chef must perform the following operation exactly once: - choose an integer $k$ ($2 \le k \le n$) - choose $k$ **increasing** valid indices of sequences $1 \leq i_1 < i_2 < \dots < i_k \leq n$ - choose $k$ arbitrary valid indices