Peaks

Byteasar works at the visitor center of Bytemountains National Park. Bytemountains has $n$ peaks, and some pairs of peaks are joined by trails of varying difficulty.

Tourists keep asking Byteasar the same kind of question: starting from a given peak and walking only along trails whose difficulty does not exceed a chosen limit, what is the height of the $k$-th highest peak that can be reached?

A peak is reachable from the starting peak when you can walk to it along a sequence of trails, each with difficulty at most the given limit. The starting peak itself is always considered reachable. Help Byteasar answer every question.

The first line contains three integers $n$, $m$, and $q$ ($1 \le n \le 100000$, $1 \le m, q \le 500000$): the number of peaks, the number of trails, and the number of questions. Peaks are numbered from $1$ to $n$.

The second line contains $n$ integers $h_1, h_2, \dots, h_n$ ($1 \le h_i \le 10^9$), the height of each peak.

Each of the next $m$ lines contains three integers $a$, $b$, and $c$ ($1 \le a, b \le n$, $a \ne b$, $1 \le c \le 10^9$), describing a bidirectional trail between peaks $a$ and $b$ with difficulty $c$; a larger $c$ means a harder trail. Two peaks may be joined by more than one trail.

Each of the next $q$ lines contains three integers $v$, $x$, and $k$ ($1 \le v \le n$, $1 \le x \le 10^9$, $1 \le k \le n$): starting from peak $v$ and using only trails of difficulty at most $x$, report the height of the $k$-th highest reachable peak.

Print $q$ lines. The $i$-th line must hold the answer to the $i$-th question: the height of the $k$-th highest peak reachable under that question's conditions. If fewer than $k$ peaks are reachable, print $-1$ instead.