P4134 [BJOI2012] Lianliankan

Among IQ-test problems there is often an elimination game. But this round of Lianliankan is not the visual-matching game on QQ. Our rule is: given all integers in the closed interval $[a, b]$, if there exist two numbers $x$, $y$ ($x > y$) such that their square difference $x^2 - y^2$ is a perfect square $z^2$, and $y$ and $z$ are coprime, then you may connect $x$ and $y$, remove them together, and gain $x + y$ points. The goal is to maximize the number of removable pairs, and subject to that, maximize the total score. Try to figure it out.

One line with two integers, denoting $a$ and $b$.

Two integers: the number of pairs that can be removed, and, under that condition, the maximum total score.

Constraints: - For $30\%$ of the testdata, $1 \le a, b \le 100$. - For $100\%$ of the testdata, $1 \le a, b \le 1000$. Translated by ChatGPT 5