Consider you have a set \(A\). A Good Range is the largest range that contains only one element from the set \(A\).

Now you are provided with the number range \(1\) to \(N\) and \(M\) queries. In each query, an integer \(X\) is added to set \(A\) and for each query, you have to output the sum of left and right border indices of all the Good Ranges.

For example. $$N$$ = $$10$$, and in the first query $$2$$ is added to set \(A\). The Good Ranges contain the range $$[1,10]$$ and the sum is $$11$$. Here $$[2,2]$$ is also a range containing only one element from the set but it isn't the largest one. Now suppose $$5$$ is added to the set, then the largest range containing only $$2$$ is $$[1,4]$$ and largest containing only $$5$$ is $$[3,10]$$, so the sum is $$1+4+3+10 = 18$$.

Note: Set contains only distinct elements.

INPUT:

The first line contains two integers $$N$$ and $$M$$.
Next, $$M$$ lines contain one integer $$X$$

OUTPUT:

For each query print one integer, the sum of all the border indices of the Good Ranges.

Note: Queries may have some numbers repeated.

CONSTRAINTS:

$$1 \le N,M \le 10^6$$
$$1 \le X \le N$$