Binary Sum

You're given two integers $N$ and $K$. Your task is to determine if there exists a binary string $S$ of length $N$ such that: - $S_1 + S_2 + S_3 + \ldots + S_N = K$, i.e, the sum of all the digits of the string equals $K$; and - $S_i \neq S_{i+1}$ for every $1 \leq i \lt N$, meaning that no two adjacent digits are equal. ### Input - The first line of input will contain a single integer $T$, denot