Red Blue Tree

You 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 ≥ 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.

Input

The first line of the input consists of two integers n and k (2 ≤ n ≤ 10^{5}, -n ≤ k ≤ n) — the number of nodes and the initial parameter k.

Each of the next n - 1 lines contains two integers u and v (1 ≤ u,v ≤ 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 ≤ s_i ≤ 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 ≤ q ≤ 10^5), the number of queries.

q lines follow, each containing a query in one of the following queries:

• 1 v (1 ≤ v ≤ n): print the color of node v;
• 2 v c (1 ≤ v ≤ 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 ≤ h ≤ n): update the current value of k to h.

Output

For each query of the first type, print 0 if the color of vertex v is red, and 1 otherwise.

Example

Input

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

inputFormat

Input

The first line of the input consists of two integers n and k (2 ≤ n ≤ 10^{5}, -n ≤ k ≤ n) — the number of nodes and the initial parameter k.

Each of the next n - 1 lines contains two integers u and v (1 ≤ u,v ≤ 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 ≤ s_i ≤ 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 ≤ q ≤ 10^5), the number of queries.

q lines follow, each containing a query in one of the following queries:

• 1 v (1 ≤ v ≤ n): print the color of node v;
• 2 v c (1 ≤ v ≤ 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 ≤ h ≤ n): update the current value of k to h.

outputFormat

Output

For each query of the first type, print 0 if the color of vertex v is red, and 1 otherwise.

Example

Input

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

样例

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

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