Drbalance

A plus/minus string is a string in which each character is either a '+' or a '-'.

The balance of a plus/minus string is computed as the number of '+' characters minus the number of '-' characters.

For example, the balance of the string "++-+" is 3-1 = 2, and the balance of the string "---" is 0-3 = -3.

The prefix of a string S is any string that can be obtained by removing some (possibly none, possibly all) characters from the end of S. For example, the prefixes of the string "++-+" are the strings "++-+", "++-", "++", "+", and "".

Given a plus/minus string, its negativity is the number of its prefixes that have a negative balance. For example, the negativity of the string "++-+" is 0, as none of its prefixes have a negative balance. The negativity of the string "---" is 3. Its three prefixes with a negative balance are "-", "--", and "---".

You are given a String s that is a plus/minus string. You are also given an int k. Your goal is to change s into a string with negativity at most k. In other words, you want to change s into a string that has at most k prefixes that have a negative balance.

In order to change s you are going to perform a sequence of zero or more steps. In each step you can change a single '-' character in s into a '+' or vice versa. Compute and return the smallest number of steps needed.