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Proof
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
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I am really confused about what u r actually trying to learn? Is it English or how to write a blog or how to solve a problem which doesn't have any description but has a proof?