Description
Hey? Everyone... Help me with this problem.
Boleyn Su runs a company called Acme. There are N employees in the company, and each one of them is represented by a unique employee id whose range lies in [1, N]. Being the head of company, Boleyn's employee id is 1.
Each employee, except Boleyn, has exactly one direct superior. This means that the hierarchial structure of the company is like a tree, where
Boleyn, employee id 1, represents the root node.
Each pair of employee is directly or indirectly connected to one another.
There is no cycle.
Let's represent the salary by the array s = {s[1], s[2], s[3]..., s[N]}, where s[i] is the salary of the ith employee. Salary structure in the company is non-uniform. Even a subordinate may get a higher salary than her superior. Some of the employees in Acme are curious about who gets the kth lowest salary among her subordinates. Help them in solving their query.
Note
1st lowest salary is equivalent to lowest salary, 2nd lowest means lowest salary which is greater that 1st lowest salary, and so on.
Salary of each employee is different.
It is not necessary that the people who are placed higher on hierarchy will have a greater salary than their subordinates.
Input Format
The first line contains two space separated integers, N Q, where N is the number of employees in Acme, and Q is the number of queries.
Then follows N-1 lines. Each of these lines contain two space separated integers, u p, where p is the superior of u. u and p are employees id.
In the next line there are N space separated integers, s[1] s[2] ... s[n], where s[i], i ∈ [1..N], is the salary of ith employee.
Then, Q queries follow. Each query contains two space separated integers, v k. See output format for it's definition.
Output format
For the first query, print the id of employee who has the kth lowest salary among the subordinates of v.
For the subsequent queries, we need to find the kth lowest salary of the subordinates of v+d, where d is the answer of previous query.
Constraints
1 ≤ N ≤ 3104
1 ≤ Q ≤ 3104
1 ≤ s[ i ] ≤ 109, i ∈ [1..N]
s[ i ] ≠ s[ j ], 1 ≤ i < j ≤ N
1 ≤ u, p ≤ N, u ≠ p
-N ≤ d ≤ N
For 1st query, 1 ≤ v ≤ N
For later queries, 1 ≤ v+d ≤ N
For each query, 1 ≤ K ≤ Number_of_subordinates
Sample Input
8 7
2 1
3 2
4 2
7 4
8 4
5 1
6 5
70 40 60 80 10 20 30 50
2 1
-6 5
-4 1
-5 3
2 1
-5 4
2 2
Sample Output
7
8
7
3
6
2
8