CF1575E.Eye-Pleasing City Park Tour

There is a city park represented as a tree with $n$ attractions as its vertices and $n - 1$ rails as its edges. The $i$-th attraction has happiness value $a_i$.

Each rail has a color. It is either black if $t_i = 0$, or white if $t_i = 1$. Black trains only operate on a black rail track, and white trains only operate on a white rail track. If you are previously on a black train and want to ride a white train, or you are previously on a white train and want to ride a black train, you need to use $1$ ticket.

The path of a tour must be a simple path — it must not visit an attraction more than once. You do not need a ticket the first time you board a train. You only have $k$ tickets, meaning you can only switch train types at most $k$ times. In particular, you do not need a ticket to go through a path consisting of one rail color.

Define $f(u, v)$ as the sum of happiness values of the attractions in the tour $(u, v)$, which is a simple path that starts at the $u$-th attraction and ends at the $v$-th attraction. Find the sum of $f(u,v)$ for all valid tours $(u, v)$ ($1 \leq u \leq v \leq n$) that does not need more than $k$ tickets, modulo $10^9 + 7$.

有一座城市公园，其结构是一棵包含 $n$ 个景点（作为顶点）和 $n - 1$ 条轨道（作为边）的树。第 $i$ 个景点的幸福值为 $a_i$。

每条轨道具有某种颜色：若 $t_i = 0$，则为黑色；若 $t_i = 1$，则为白色。黑色列车仅能在黑色轨道上运行，白色列车仅能在白色轨道上运行。若你此前乘坐的是黑色列车，现在想换乘白色列车，或此前乘坐的是白色列车，现在想换乘黑色列车，则需消耗 $1$ 张车票。

一次游览的路径必须是一条简单路径——即不能重复访问任一景点。首次登车无需消耗车票。你总共仅有 $k$ 张车票，意味着最多只能切换列车类型 $k$ 次。特别地，若整段路径仅使用一种颜色的轨道，则无需消耗任何车票。

定义 $f(u, v)$ 为从第 $u$ 个景点出发、到第 $v$ 个景点结束的游览路径（即简单路径）所经过的所有景点的幸福值之和。请计算所有满足条件的游览路径 $(u, v)$（其中 $1 \leq u \leq v \leq n$）对应的 $f(u,v)$ 之和，并对 $10^9 + 7$ 取模。

The first line contains two integers $n$ and $k$ ($2 \leq n \leq 2 \cdot 10^5$, $0 \leq k \leq n-1$) — the number of attractions in the city park and the number of tickets you have.

The second line contains $n$ integers $a_1, a_2,\ldots, a_n$ ($0 \leq a_i \leq 10^9$) — the happiness value of each attraction.

The $i$-th of the next $n - 1$ lines contains three integers $u_i$, $v_i$, and $t_i$ ($1 \leq u_i, v_i \leq n$, $0 \leq t_i \leq 1$) — an edge between vertices $u_i$ and $v_i$ with color $t_i$. The given edges form a tree.

第一行包含两个整数 $n$ 和 $k$（$2 \leq n \leq 2 \cdot 10^5$，$0 \leq k \leq n-1$）—— 分别表示城市公园中景点的数量以及你拥有的门票数量。

第二行包含 $n$ 个整数 $a_1, a_2,\ldots, a_n$（$0 \leq a_i \leq 10^9$）—— 表示每个景点带来的快乐值。

接下来的 $n - 1$ 行中，第 $i$ 行包含三个整数 $u_i$、$v_i$ 和 $t_i$（$1 \leq u_i, v_i \leq n$，$0 \leq t_i \leq 1$）—— 表示顶点 $u_i$ 与 $v_i$ 之间的一条边，其颜色为 $t_i$。所给的边构成一棵树。

Output an integer denoting the total happiness value for all valid tours $(u, v)$ ($1 \leq u \leq v \leq n$), modulo $10^9 + 7$.

输出一个整数，表示所有有效路径 $(u, v)$（其中 $1 \leq u \leq v \leq n$）的总幸福值，对 $10^9 + 7$ 取模。