F. Subtree Minimum Query
time limit per test
6 seconds
memory limit per test
512 megabytes
input
standard input
output
standard output

You are given a rooted tree consisting of n vertices. Each vertex has a number written on it; number ai is written on vertex i.

Let's denote d(i, j) as the distance between vertices i and j in the tree (that is, the number of edges in the shortest path from i to j). Also let's denote the k-blocked subtree of vertex x as the set of vertices y such that both these conditions are met:

• x is an ancestor of y (every vertex is an ancestor of itself);
• d(x, y) ≤ k.

You are given m queries to the tree. i-th query is represented by two numbers xi and ki, and the answer to this query is the minimum value of aj among such vertices j such that j belongs to ki-blocked subtree of xi.

Write a program that would process these queries quickly!

Note that the queries are given in a modified way.

Input

The first line contains two integers n and r (1 ≤ r ≤ n ≤ 100000) — the number of vertices in the tree and the index of the root, respectively.

The second line contains n integers a1, a2, ..., an (1 ≤ ai ≤ 109) — the numbers written on the vertices.

Then n - 1 lines follow, each containing two integers x and y (1 ≤ x, y ≤ n) and representing an edge between vertices x and y. It is guaranteed that these edges form a tree.

Next line contains one integer m (1 ≤ m ≤ 106) — the number of queries to process.

Then m lines follow, i-th line containing two numbers pi and qi, which can be used to restore i-th query (1 ≤ pi, qi ≤ n).

i-th query can be restored as follows:

Let last be the answer for previous query (or 0 if i = 1). Then xi = ((pi + last) modn) + 1, and ki = (qi + last) modn.

Output

Print m integers. i-th of them has to be equal to the answer to i-th query.

Example
Input
5 21 3 2 3 52 35 13 44 121 22 3
Output
25