Largest K

You are given integers $X$ and $Y$ $(2 \leq X, Y \leq 10^9)$. Find the largest integer $K$ such that there exists a **binary** string $S$, where: - The count of $\text{0}$s in $S$ is $X$; - The count of $\text{1}$s in $S$ is $Y$; - There are **atleast** $K$ $\text{1}$s between any two occurrences of $\text{0}s$ in $S$. ### Input - The first line contains a single integer $T$, denoting the number