Tavas lives in Tavaspolis. Tavaspolis has n cities numbered from 1 to n connected by n - 1 bidirectional roads. There exists a path between any two cities. Also each road has a length. Tavas' favorite strings are binary strings (they contain only 0 and 1). For any binary string like s = s 1 s 2... s k , T(s) is its Goodness . T(s) can be calculated as follows: Consider there are exactly m blocks of 1s in this string (a block of 1s in s is a maximal consecutive substring of s that only contains 1) with lengths x 1, x 2, ..., x m . Define where f is a given sequence (if m = 0, then T(s) = 0). Tavas loves queries. He asks you to answer q queries. In each query he gives you numbers v, u, l and you should print following number: Consider the roads on the path from city v to city u : e 1, e 2, ..., e x . Build the binary string b of length x such that: b i = 1 if and only if l ≤ w(e i ) where w(e) is the length of road e . You should print T(b) for this query.

输入描述:

The first line of input contains integers n and q (2 ≤ n ≤ 105 and 1 ≤ q ≤ 105).The next line contains n - 1 space separated integers f1, f2, ..., fn - 1 (fi ≤ 1000).The next n - 1 lines contain the details of the roads. Each line contains integers v, u and w and it means that there's a road between cities v and u of length w (1 ≤ v, u ≤ n and 1 ≤ w ≤ 109).The next q lines contain the details of the queries. Each line contains integers v, u, l (1 ≤ v, u ≤ n, v ≠ u and 1 ≤ l ≤ 109).

输出描述:

Print the answer of each query in a single line.