Counting Triangles 101

A set $S$ is said to be *good* iff : - For all $x, y, z \in S$, such that $x \ne y, x \ne z, y \ne z$; $(x, y, z)$ are the side lengths of a valid non-degenerate triangle. Count the number of sets $S$ of $N$ distinct integers which are *good*, and all elements of the set $S_i$ satisfy $1 \le S_i \le M$. Since the answer may be large, output it modulo $10^9 + 7$. ### Input - The first line of