Convert string

You are given a binary string $S$ of length $N$. For a positive integer $k$, you can perform the following operation on string $S$: - Choose $k$ elements from the string $S$; - Perform a total of $k$ flips on the chosen $k$ elements. A flip changes a `0` to `1` and vice versa. Note that you can use multiple flips on the same element. Find the count of all such $k$ in range $[1,N]$, such that, y