Compute Maximum Currency Exchange Rate

You are given a set of n currencies, labeled from 0 to n - 1, and m direct exchange rates between some pairs of them. Each direct exchange rate specifies how many units of one currency you can obtain for 1 unit of another.

Formally:

• An exchange rate is represented as a triple (u, v, r), meaning that if you start with 1 unit of currency u, you can directly obtain r units of currency v.
• You can perform a sequence of exchanges, chaining them together. If you exchange from u to v with rate r1 and then from v to w with rate r2, the effective rate from u to w along that path is r1 * r2.
• You must assume that you do not revisit the same currency within a single exchange path (i.e., paths are simple, without repeated nodes). This ensures the maximum rate is always finite.

You are also given a starting currency A and a target currency B. Your goal is to determine the maximum possible amount of currency B you can obtain, starting with 1 unit of currency A, by performing zero or more allowed exchanges.

Constraints and Edge Cases

• If A is the same as B (A == B), you may choose to perform zero exchanges. In this scenario, you can always end with at least 1 unit of B, so the minimum answer is 1.0.
• If it is impossible to reach currency B starting from A via any sequence of exchanges, you should return -1.0.

Input Format (Example Specification)

• An integer n representing the total number of currencies.
• An integer m representing the number of direct exchange rates.
• The next m lines each contain three values: u v r.
  • u and v are integers in the range [0, n-1].
  • r is a real number greater than 0, representing the direct exchange rate from u to v.
• The last line contains two integers A B, representing the start and target currencies.

Output Format

• Output a single real number: the maximum amount of currency B obtainable from 1 unit of currency A.
• If B is unreachable from A, output -1.0.

Example

Suppose:

• n = 3 (currencies 0, 1, 2)
• m = 3
• Exchange rates:
  • 0 1 2.0 (1 unit of 0 → 2 units of 1)
  • 1 2 3.0 (1 unit of 1 → 3 units of 2)
  • 0 2 4.0 (1 unit of 0 → 4 units of 2)
• A = 0, B = 2.

Possible paths from 0 to 2:

• Direct: 0 -> 2 with rate 4.0 → get 4.0 units.
• Via 1: 0 -> 1 -> 2 with rate 2.0 * 3.0 = 6.0 → get 6.0 units.

The maximum achievable amount of currency 2 is 6.0.