Royal Tax

The kingdom of Nlogônia is rich and its people are educated and content, but the King is a tyrant when the subject is taxes. At the end of every year, each city of the kingdom owes a fixed amount of gold in taxes. When collection time arrives, the King sends the royal carriage along the roads of the kingdom to gather the gold that is owed.

Each road connects two different cities and can be driven in both directions. The road network lets the carriage reach any city from any other city, possibly through intermediate cities, and there is exactly one path between two different cities.

Every city has a royal vault that stores tax gold. The vaults are enormous, so each one can hold all the gold owed by the entire kingdom. The carriage leaves the capital, drives the roads and visits cities to load the gold they owe. If that helps, it may leave part of the collected gold in any royal vault for a while. When the collection ends, all the gold owed by all the cities must be stored in the vault of the capital.

You are given the amount of gold each city owes in kg, the list of roads with their lengths in km, and the carrying capacity of the royal carriage in kg. Determine the minimum distance the carriage has to travel to collect all the gold that is owed.

The first line contains two integers $N$ and $C$, the number of cities and the carrying capacity of the carriage ($2 \le N \le 10^4$, $1 \le C \le 100$). The capital is city 1 and the other cities are numbered from 2 to $N$.

The second line contains $N$ integers $E_1, E_2, \dots, E_N$, where $E_i$ is the amount of gold city $i$ owes, in kg ($0 \le E_i \le 100$).

Each of the next $N-1$ lines contains three integers $A$, $B$ and $L$, meaning that a road of length $L$ km connects city $A$ and city $B$ ($1 \le A, B \le N$, $A \ne B$, $1 \le L \le 100$).

Print on the first line a single integer, the minimum distance in km that the royal carriage has to travel to collect all the tax that is owed.