Digit occurrence Sum
Description
Given $n$ distinct non-negative currently available integers $a_1, a_2, ..., a_n$. Define the function $count(x)$ as the number of times the digit $x$ appears in all currently available integers. For any integer $k$, $f(k)$ is defined as the sum of $count(x)$ for each digit $x$ in $k$.
For example, let's consider the currently available integers: $70, 123, 311, 125$. In this case, $count(0) = 1$, $count(1) = 4$, and so on. For $f(311)$, we have $count(3) + count(1) + count(1) = 2 + 4 + 4 = 10.$
You will be given $q$ queries, each of which can be one of the following three types:
1. $+\;k$: Add integer $k$ to the currently available integers if it's not already present. If $k$ is already in the list, remove it.
2. $-\;k$: Delete the $k$-th largest integer from the currently available integers. If there are fewer than $k$ integers available, skip this operation.
3. $?\;k$: Print $f(k)$ if $k$ is currently available among the integers. If $k$ is not available, print $-1$.
The first line consists of two integers $n, q$.
Second line consists of $n$ integers $a_1,a_2,\cdots,a_n$.
Next $q$ lines each consist of $-\;k$, $+\;k$ or $?\;k$.
$1 \leq n, q \leq 3 \times 10^5$
$1 \leq a_i \leq 2 \times 10^9$
For each "$?\;k$" In the query, Print $f(k)$ if $k$ is currently available. Otherwise print $-1$.
Input
The first line consists of two integers $n, q$.
Second line consists of $n$ integers $a_1,a_2,\cdots,a_n$.
Next $q$ lines each consist of $-\;k$, $+\;k$ or $?\;k$.
$1 \leq n, q \leq 3 \times 10^5$
$1 \leq a_i \leq 2 \times 10^9$
Output
For each "$?\;k$" In the query, Print $f(k)$ if $k$ is currently available. Otherwise print $-1$.
4 6
70 123 311 125
? 123
- 2
? 123
+ 234
- 3
? 123
8
6
-1