EDYOOCATIONAL CONTESNT #3
Let $$$y_1$$$ be a point on the coordinate plane where $$$y_1$$$ is more optimal than some $$$y_j$$$.
This can only be true if $$$y_1 \cdot y_j \equiv 2 \text{ }(\text{mod } 10^9 + 7)$$$.
left as an exersise for the reader lol
Codeforces Round 946 Solution Discussion