Balance the Game Board

A game board consists of N+1 fields, numbered from 0 to N from left to right. One letter ("a" or "b") is written between every two adjacent fields. The letters on the board are described by a string L of length N, where L[K] (for K within the range [0..N-1]) is the letter between fields K and K+1.

For example, given L = "aaabab" and N = 6, the game board at the beginning looks like this:

a a a b a b

0 1 2 3 4 5 6

A game piece is placed at start. It can move left or right, flipping the letter it crosses ("a" → "b" and "b" → "a"). The objective is to find the minimum number of moves needed to balance the count of "a" and "b". If it's impossible, return -1

Write a function that, given a string L of length N and an integer start, returns the minimum number of moves such that, after those moves, there will be the same number of letters "a" and "b" on the board (or returns -1 if it is impossible).