H. Red Blue Treetime limit per test5 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputYou are given a tree of n nodes. The tree is rooted at node 1, which is not considered as a leaf regardless of its degree.Each leaf of the tree has one of the two colors: red or blue. Leaf node v initially has color s_{v}.The color of each of the internal nodes (including the root) is determined as follows.   Let b be the number of blue immediate children, and r be the number of red immediate children of a given vertex.  Then the color of this vertex is blue if and only if b - r \ge k, otherwise red. Integer k is a parameter that is same for all the nodes.You need to handle the following types of queries:   1 v: print the color of node v;  2 v c: change the color of leaf v to c (c = 0 means red, c = 1 means blue);  3 h: update the current value of k to h. InputThe first line of the input consists of two integers n and k (2 \le n \le 10^{5}, -n \le k \le n) — the number of nodes and the initial parameter k.Each of the next n - 1 lines contains two integers u and v (1 \le u,v \le n), denoting that there is an edge between vertices u and v.The next line consists of n space separated integers — the initial array s (-1 \le s_i \le 1). s_{i} = 0 means that the color of node i is red. s_{i} = 1 means that the color of node i is blue. s_{i} = -1 means that the node i is not a leaf.The next line contains an integer q (1 \le q \le 10^5), the number of queries.q lines follow, each containing a query in one of the following queries:   1 v (1 \le v \le n): print the color of node v;  2 v c (1 \le v \le n, c = 0 or c = 1): change the color of leaf v to c (c = 0 means red, c = 1 means blue). It is guaranteed that v is a leaf;  3 h (-n \le h \le n): update the current value of k to h. OutputFor each query of the first type, print 0 if the color of vertex v is red, and 1 otherwise.ExampleInput
5 2
1 2
1 3
2 4
2 5
-1 -1 0 1 0
9
1 1
1 2
3 -2
1 1
1 2
3 1
2 5 1
1 1
1 2
Output
0
0
1
1
0
1
Note Figures:(i) The initial tree (ii) The tree after the 3rd query (iii) The tree after the 7th query    
5 2
1 2
1 3
2 4
2 5
-1 -1 0 1 0
9
1 1
1 2
3 -2
1 1
1 2
3 1
2 5 1
1 1
1 2

0 0 1 1 0 1 
['data structures', 'implementation', 'trees', '*3500']