Problem Description

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 $10^{9}+7$.

Input Format

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

Output Format

One integer, representing the answer.

3 3

4

5 1

453

Hint

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