You are given an integer $n$, representing $n$ units numbered from $0$ to $n - 1$.

You are also given a 2D integer array conversions of length $n - 1$, where conversions[i] = [sourceUnit_i, targetUnit_i, conversionFactor_i] indicates that $1$ unit of sourceUnit_i is equal to conversionFactor_i units of targetUnit_i.

You are also given a 2D integer array queries, where queries[j] = [unitA_j, unitB_j] asks for the number of units of unitB_j that equal $1$ unit of unitA_j.

Return an array of integers representing the answer to each query. Since the answer may be a fractional value or very large, compute the result modulo $10^9 + 7$ by returning the answer multiplied by the modular multiplicative inverse modulo $10^9 + 7$.

Note: The division $\frac{A}{B} \pmod{10^9 + 7}$ is calculated as $(A \times B^{-1}) \pmod{10^9 + 7}$, where $B^{-1}$ is the modular multiplicative inverse of $B$ modulo $10^9 + 7$.

Constraints:

• $2 \leq n \leq 10^5$

• conversions.length $= n - 1$

• $0 \leq$ sourceUnit_i, targetUnit_i $< n$

• $1 \leq$ conversionFactor_i $\leq 10^9$

• $1 \leq q \leq 10^5$

• queries.length $= q$

• $0 \leq$ unitA_j, unitB_j $< n$

• It is guaranteed that unit $0$ can be uniquely converted into any other unit through a combination of forward or backward conversions.

Now, 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 of how to solve this problem.

Implement your solution in the following coding playground.