Balanced Numbers in a Permutation

You are given a permutation p of length n. A number k is called balanced if there exists a contiguous subarray p[l..r] whose elements form a permutation of the numbers 1, 2, ..., k. For every k from 1 to n, determine whether k is balanced. Return a binary string of length n where the kth character is:

• "1" if k is balanced
• "0" otherwise A permutation of length n contains every integer from 1 to n exactly once.

1, 3, and 4 are balanced, but 2 is not. For example, [1, 3, 2] is a contiguous permutation of 1..3.

For every k from 1 to 5, the values 1..k occupy a contiguous block somewhere in the permutation.

Only 1 and 4 are balanced. The values 1..2 and 1..3 do not fit inside a contiguous block of lengths 2 and 3.