Rearranging a Bit String

A bit string is a string made only of 0 and 1. You are given one bit string and must turn it into a fixed target string. The only operation you may use is swapping two adjacent bits.

The starting string is given as a plain sequence of bits. The target string is given as a run code instead. A run code lists the lengths of the consecutive blocks of 0s or 1s in the string, in order from the left. For example, the run code of "011100" is "1 3 2". Two strings always share a given run code: one that starts with 0 and one that starts with 1.

Compute the smallest number of operations needed to turn the starting string into the target string.

The first line has two integers $N$ ($1 \le N \le 15$) and $M$ ($1 \le M \le N$). The second line has the $N$ bits of the starting string, separated by spaces. The third line has the run code of the target string as $M$ integers, in order.

Every number in the run code is at least 1, and the numbers add up to $N$. The given bit string can always be turned into the string that the run code describes.

Print the smallest number of operations needed.

Take the bit string "100101" and a target run code of "1 3 2". The two possible target strings are "011100" and "100011". Reaching "011100" takes 4 operations, while reaching "100011" takes only 1. The answer is therefore 1.