Query on the subtree

bobo has a tree, whose vertices are conveniently labeled by 1,2,…,n. At the very begining, the i-th vertex is assigned with weight w_i.

There are q operations. Each operations are of the following 2 types:

Change the weight of vertex v into x (denoted as "! v x"),
Ask the total weight of vertices whose distance are no more than d away from vertex v (denoted as "? v d").

Note that the distance between vertex u and v is the number of edges on the shortest path between them.

The input consists of several tests. For each tests:

The first line contains n,q (1≤n,q≤10⁵). The second line contains n integers w₁,w₂,…,w_n (0≤w_i≤10⁴). Each of the following (n - 1) lines contain 2 integers a_i,b_i denoting an edge between vertices a_i and b_i (1≤a_i,b_i≤n). Each of the following q lines contain the operations (1≤v≤n,0≤x≤10⁴,0≤d≤n).

For each tests:

For each queries, a single number denotes the total weight.

4 3
1 1 1 1
1 2
2 3
3 4
? 2 1
! 1 0
? 2 1
3 3
1 2 3
1 2
1 3
? 1 0
? 1 1
? 1 2

3
2
1
6
6

Xiaoxu Guo (ftiasch)

2014 Multi-University Training Contest 5