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Problem Background

Muxue the youth discovered a kind of magical bracket: each '(' contains +1 magical energy, each ')' contains -1 magical energy. By flipping brackets, he can adjust the total magical energy of the whole sequence.

Problem Description

Muxue has a kind of magical bracket: '(' has a magic value of 1, ')' has a magic value of -1. The magic value of a bracket sequence is defined as the sum of the magic values of all brackets.

Muxue can perform magic: choose a position in the sequence and flip the bracket at that position ('(' becomes ')', ')' becomes '('), consuming 1 point of magical energy.

Now there is a bracket sequence of length n. Muxue wants to know the minimum amount of magical energy he needs to consume to make the magic value of the sequence exactly equal to k.

Note: The flipped sequence does not need to be a valid bracket sequence; it only needs to have a magic value equal to k.

Input Format

First line: two integers n and k (1 ≤ n ≤ 10^5, -n ≤ k ≤ n)
Second line: a bracket string of length n

Output Format

An integer, representing the minimum magical energy; if impossible, output -1

Sample Input and Output #1

Input #1

5 1
()()(

Output #1

1

Explanation/Notes

Explanation for Sample 1: The current magic value is 1+(-1)+1+(-1)+1=1, which already equals k, so no operation is needed.