1146E · Hot is Cold

Problem: You are given an array of $n$ integers $a_1, a_2, \ldots, a_n$.

You will perform $q$ operations. In the $i$-th operation, you have a symbol $s_i$ which is either "<" or ">" and a number $x_i$.

You make a new array $b$ such that $b_j = -a_j$ if $a_j s_i x_i$ and $b_j = a_j$ otherwise (i.e. if $s_i$ is '>', then all $a_j > x_i$ will be flipped). After doing all these replacements, $a$ is set to be $b$.

You want to know what your final array looks like after all operations.

Input Format: The first line contains two integers $n,q$ ($1 \leq n,q \leq 10^5$) — the number of integers and the number of queries.

The next line contains $n$ integers $a_1, a_2, \ldots, a_n$ ($-10^5 \leq a_i \leq 10^5$) — the numbers.

Each of the next $q$ lines contains a character and an integer $s_i, x_i$. ($s_i \in \{<, >\}, -10^5 \leq x_i \leq 10^5$) – the queries.

Output Format: Print $n$ integers $c_1, c_2, \ldots, c_n$ representing the array after all operations.

Note: In the first example, the array goes through the following changes:

• Initial: $[-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5]$
• $> 2$: $[-5, -4, -3, -2, -1, 0, 1, 2, -3, -4, -5]$
• $> -4$: $[-5, -4, 3, 2, 1, 0, -1, -2, 3, -4, -5]$
• $< 5$: $[5, 4, -3, -2, -1, 0, 1, 2, -3, 4, 5]$