Tree and paths of length two

Given $N$ and $S$, write a program that decides whether a tree satisfying both of the following conditions exists.

• The tree has $N$ nodes.
• The number of simple paths of length 2 is $S$.

A simple path is a path that does not pass through the same vertex more than once. The length of a path is the number of edges on it, so a simple path of length 2 joins three distinct vertices.

Direction does not matter in a path. A-B-C and C-B-A count as the same path.

The first line contains $N$ and $S$ separated by a space. ($1 \le N \le 50$, $1 \le S \le 1000$)

Print 1 if such a tree can be built, and 0 if it cannot.