Poisonous Labyrinth

BThero needs to escape from a labyrinth shaped like a tree with $n$ vertices and $n-1$ edges. Each edge has a length. The vertices hold $2m$ poison vials in total: two vials of each of the $m$ poison types.

When BThero enters a vertex for the first time, he drinks all the vials in that vertex immediately. If he enters a vertex he has already visited, there are no vials left to drink there.

Drinking a vial of a poison type he has not drunk before poisons him. To cure it, he must find and drink the other vial of the same type.

BThero starts at vertex $s$ and drinks the vials there at once. He then keeps moving through vertices until he is no longer poisoned. After that, he returns to vertex $s$ and leaves the labyrinth.

Find the starting vertex $s$ that minimizes the total distance BThero travels along an optimal route.

The first line contains two integers $n$ and $m$ ($2 \le n \le 2 \cdot 10^5$, $1 \le m \le 2 \cdot 10^5$), the number of vertices and the number of poison types.

Each of the next $n-1$ lines contains three integers $u_i$, $v_i$, and $w_i$ ($1 \le u_i, v_i \le n$, $1 \le w_i \le 10^9$). This describes a bidirectional edge between vertices $u_i$ and $v_i$ with length $w_i$.

Each of the next $m$ lines contains two integers $a_j$ and $b_j$ ($1 \le a_j, b_j \le n$), the two vertices where the vials of poison type $j$ are located. It is possible that $a_j = b_j$. In that case, BThero is poisoned as soon as he enters the vertex and is cured immediately.

Print one integer on a line: the minimum distance BThero must travel to cure all poisons when he starts from the optimal vertex.