### Problem Description

Cuber QQ always envies those Kejin players, who pay a lot of RMB to get a higher level in the game. So he worked so hard that you are now the game designer of this game. He decided to annoy these Kejin players a little bit, and give them the lesson that RMB does not always work.

This game follows a traditional Kejin rule of “when you are level i, you have to pay ai RMB to get to level i+1”. Cuber QQ now changed it a little bit: “when you are level i, you pay ai RMB, are you get to level i+1 with probability pi; otherwise you will turn into level xi (xi≤i)”.

Cuber QQ still needs to know how much money expected the Kejin players needs to “ke’’ so that they can upgrade from level l to level r, because you worry if this is too high, these players might just quit and never return again.