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 $$$10^9 + 7$$$.

Input

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.

Output

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

Eye-Pleasing City Park Tour

Examples