P6596 How Many of Them

In an undirected connected graph, if removing an edge makes the graph split into two disconnected parts, then this edge is called a bridge. Find the number of undirected connected graphs that satisfy the following conditions: 1. The graph consists of $n$ labeled vertices. 2. The number of bridges is at most $m$. 3. There are no multiple edges and no self-loops. Output the answer modulo $10^{9}+7$.

Only one line with two integers $n$ and $m$.

One integer, representing the answer.

Constraints: $2 \le n \le 50$, $0 \le m \le \dfrac{n(n-1)}{2}$. Source: Gennady Korotkevich (tourist), ITMO University. Translated by ChatGPT 5