Your are given a Tree, a connected undirected graph consisting of N nodes, N-1 undirected edges and no cycles. Nodes are numbered from 1 to N.
A simple path between two nodes in a tree is a path between the two nodes consisting of no repeating nodes. 
More formally, Simple path between two nodes a and b is a sequence of nodes V₁ V₂, ..., V_m such that

•  All V_i are distinct.
•  V_i and V_i+1 are connected by an edge for 1 \(\leq\) i \(\leq\) m-1.
•  V₁ = a and V_m = b.

For any pair of nodes in a tree, this path is unique.

You are given M pair of nodes by means of two arrays L and R where (L_i, R_i) represents the i^th pair of nodes. Each pair represents a simple path between its nodes.

For each edge,report whether it is a part of at least one of the given simple paths or not.

Input: 
First line consists of two space separated integers, N and M, where N represent the number of nodes, and M represent the number of simple paths.
Next N-1 lines consist of two space separated integers each, representing two nodes connected by an edge.
Next line consists of M space separated integers, representing array L.
Next line consists of M space separated integers, representing array R.

Constraints:
2 \(\leq\) N \(\leq\) 10⁵
1 \(\leq\) M \(\leq\) 10⁶
1 \(\leq\) Li, Ri \(\leq\) N
The edges are guaranteed to form a valid tree.

Output:
For each edge, in the same order as they were received in input, output 
    1, if it is a part of at least one of the given simple paths
    or 0, otherwise.
For each edge, output answer in a new line.