Binary Search Counts

Problem Description

There are $n$ numbers $a_1, a_2, \dots, a_n$ and $m$ queries.

Each query gives a number $x$; you must answer, among $a_1, a_2, \dots, a_n$, how many numbers are less than $x$, equal to $x$, and greater than $x$ respectively.

Input Format

The first line contains two integers $n, m$. The next line contains $n$ integers, the sequence $a_1, a_2, \dots, a_n$.

The following $m$ lines each contain one integer $x$.

Output Format

Output $m$ lines, each containing three integers: the answer.

Sample Input

6 6
3 5 1 5 3 5
1
2
3
4
5
6

Sample Output

0 1 5
1 0 5
1 2 3
3 0 3
3 3 0
6 0 0

Constraints

For $100\%$ of the data: $1 \leq n, m \leq 2\times 10^5$, $1 \leq a_i, x \leq 10^9$.