上海市大学生程序设计竞赛 - 十二月赛

It is all choosen by Steins Gate!

As a fan of Steins Gate, you made a game with its background. The whole game world is composed of all positive integers. In the game, $1$ represents the public event, prime numbers represent events that affect the world line, and composite numbers represent world lines.

When a prime number $p$ is a factor of the composite number $c$, it means that the event $p$ can affect the world line $c$. If all events affecting a world line occur, you can choose to reach the world line. For example, reaching world line 12 requires events 2 and 3 to occur. Of course, if events 2 and 3 happen, you can reach an infinite number of world lines such as $4,6,8,9,12…$

As a game developer, you know there are $n$ world lines $a_ 1,…,a_n$ you really want to reach. Because of your excellent performance in developing the game, you get the reward opportunity of $len$: you can choose $1$ or any event as the base point $p$, and all events in the closed interval $[p + 1, p + len] $ will happen.

You want to reach all $n$ world lines, and if there are multiple choices, always give priority to the one with a larger base point. If all $n$ world lines can be reached, you should find the largest base point $p$, and you should output the total number of events that will happen (in other words, output the number of primes in $[p+1,p+len]$). Otherwise, just output $-1$ .