You are given an undirected tree with n vertices labeled from $1$ to $n$. A frog starts at vertex $1$, at time $0$, and makes one move per second.

At each step, the frog follows these rules:

1. Move to an unvisited neighbor:
   If the frog has unvisited neighbors, it jumps to one of them, chosen uniformly at random (equal probability for each choice).

2. No revisiting:
   The frog can not jump back to a vertex it has already visited.

3. Stay when stuck
   The frog will keep jumping at its current vertex if there are no unvisited neighbors.

The tree is represented as an array of edges, where edges[i] = [$a_i$, $b_i$] means an edge connecting the vertices $a_i$ and $b_i$. Your task is to return the probability that, after t seconds, the frog is on the vertex target.

Note: Your answer will be accepted if its absolute difference from the actual value is at most $10^{-5}$.

Constraints:

• 1 $\leq$ n $\leq$100

• edges.length == $n - 1$

• edges[i].length == 2

• $1$ $\leq$ $a_i$, $b_i$ $\leq$ n

• $1$$\leq$ t $\leq$ $50$

• $1 \leq$ target $\leq$n

Let’s take a moment to make sure you’ve correctly understood the problem. The quiz below helps you check if you’re solving the correct problem:

We have a game for you to play. Rearrange the logical building blocks to develop a clearer understanding on how to solve this problem.

Implement your solution in the following coding playground.