Problem Description

$n$ people are taking an elevator, where the $i$-th person gets off at the $a_i$-th floor, and $a_{1\sim n}$ forms a permutation.

The elevator is rectangular, so the $n$ people initially line up in the elevator in numerical order. The elevator will pass through floors $1$ to $n$ in ascending order.

When a person needs to get off the elevator, everyone in front of them must also temporarily get off, and they can then return to the elevator in any order. Those behind do not need to and will not get off.

If the people who temporarily get off always return to the elevator using the optimal strategy, please determine the minimum total number of times everyone gets off the elevator.

Given $q$ operations, each specifying $x_i$ to remove the person with the number $x_i$, you need to calculate the answer before the first operation and after each operation.

Input Format

The first line contains two integers $n$ and $q$.

The second line contains $n$ numbers $a_{1\sim n}$, which form a permutation of $1$ to $n$.

The third line contains $q$ numbers $x_{1\sim q}$, representing the $q$ queries.

Output Format

Output one line with $q+1$ numbers, representing the answer before the first operation and after each operation.

Sample Input and Output

Input Sample #1

5 2
3 4 1 2 5
3 2

Output Sample #1

9 6 4

Input Sample #2

7 0
4 5 2 1 6 3 7

Output Sample #2

13

Input Sample #3

3 2
3 1 2
1 2

Output Sample #3

5 2 1

Notes

Data Range

For all data, $0 \le q < n \le 10^5$.

见题面 Input 部分

见题面 Output 部分