The polynomial $P(x, y)$ satisfies the equality $P(x, y) = \begin{cases} 1 & x=y \\0 & \text{else} \end{cases}$ for $x, y \in \{0, 1, 2, \cdots, 60\}$. Additionally, the degree of $P$ in $x$ and the degree of $P$ in $y$ are both at most $60$. Find $P(61, 61)$.