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Define the score of some binary string T as the absolute difference between the number of zeroes and ones in it.
(for example, T= 010001 contains 4 zeroes and 2 ones, so the score of T is |4−2|=2).
Define the creepiness of some binary string S as the maximum score among all of its prefixes
(for example, the creepiness of S= 01001 is equal to 2 because the score of the prefix S[1…4] is 2 and the rest of the prefixes have a score of 2 or less).
Given two integers a and b, construct a binary string consisting of a zeroes and b ones with the minimum possible creepiness.