Beauty of a tree having $m$ edges and weights as $w_1, w_2 ......w_m$ is defined as $w_1 \oplus w_2 \oplus w_3... \oplus w_{n-1} \oplus w_n$. The beauty of a tree having a single vertex is $0$

You are given a weighted tree having $n$ vertices. Recall that a tree is a connected undirected graph without cycles.

You are then given $n$ edges where the $i^{th}$ edge has $w_i$ weight and connects the two vertices $a_i$ and $b_i$ 

You are also given $q$ queries. In every query you will be given a number $u$ which denotes the $u_{th}$ edge of the tree. For every query your task is to find the absolute difference between the beauty of the two components created if that edge had been removed from the tree. 

it is garaunteed that each vertex is a part of atleast one edge.

See the sample test case for further explaination

Input

The first line of the input contains two integers $n(2≤n≤2\cdot10^5)$ and $q (1≤q≤2\cdot10^5 )$ — the number of vertices in the tree and the number of queries respectively. 

The following $n−1$ lines each contain three space-separated integers, where the $i^{th}$ line containing integers $a_i(1 \leq a_i \leq n)$ , $b_i ( 1 \leq b_i \leq n )$, $w_i ( 1 \leq w_i < 10^{12})$denotes an edge from ai to bi having weight $w_i$.

The next $q$ lines contains a single integer $u ( 1 \leq u < n )$ denoting the $u^{th}$ edge that is considered to be removed for that query.

Output

For every query print the absolute difference between the beauty of the created components on a separate line