E. Mike and Foam (the principle of repulsion)

E. Mike and Foam

Mike is a bartender at Rico ' s bar. At Rico ' s, they put beer glasses in a special shelf. There isn kinds of beer at Rico ' s numbered from 1 to n. i-th kind of beer havea_i milliliters of foam on it.

Maxim is Mike ' s boss. Today he told Mike to perform Q queries. Initially the shelf is empty. In each request, Maxim gives him a numberx. If Beer number x is already in the shelf, then Mike should remove it from the shelf, otherwise he should put it In the shelf.

After all query, Mike should tell him the score of the shelf. Bears is geeks. So they think then the score of a shelfis the number of pairs (i,? J) of glasses in the shelf such thati? <? J and where is the greatest common divisor of numbersa and b.

Mike is tired. So he asked the him in performing these requests.

Input

The first line of input contains numbers n andq (1?≤? N,? q. ≤?2?x?10⁵), the number of different kinds of beer and number of queries.

The next line contains n space separated integers,a_{1,? A2,?...,? An} (1?≤? ) A_{i-≤?5?x?10⁵}), the height of foam in top of each kind of beer.

The next Q lines contain the queries. Each query consists of a single integer integerx (1?≤? x? ≤? n), the index of a beer that should is added or removed from the shelf.

Output

For each query, print the answer.

Sample Test (s) Input

5 61 2 3 4 6123451

Output

013562

Test instructions easy to understand, I will not say ...

Problem: The topic can be translated into, in a dynamic set. No more than one count. Or take out a number, the number of coprime in the remaining numbers is a number of pairs. Attention is unordered. Since the number of mass factors is very small in the data range of the topic, the complexity is largely negligible, so we are able to add to each new number. Or the number taken out of the mass factor decomposition. Then through the tolerant principle, first calculate how many of the set is not coprime, this very easy to calculate it!

(Assuming that I can't think of a way to look at my code, it's just an array to count, quite simply). I know it's not coprime. Nature will know coprime spicy!

Then subtract or add the number of coprime to the answer. Time complexity is expected 10^7 level.

E. Mike and Foam (the principle of repulsion)