CF1661F Teleporters

There are $ n+1 $ teleporters on a straight line, located in points $ 0 $ , $ a_1 $ , $ a_2 $ , $ a_3 $ , ..., $ a_n $ . It's possible to teleport from point $ x $ to point $ y $ if there are teleporters in both of those points, and it costs $ (x-y)^2 $ energy. You want to install some additional teleporters so that it is possible to get from the point $ 0 $ to the point $ a_n $ (possibly through some other teleporters) spending no more than $ m $ energy in total. Each teleporter you install must be located in an integer point. What is the minimum number of teleporters you have to install?

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