COT - Count on a tree


You are given a tree with N nodes. The tree nodes are numbered from 1 to N. Each node has an integer weight.

We will ask you to perform the following operation:

  • u v k : ask for the kth minimum weight on the path from node u to node v

Input

In the first line there are two integers N and M. (N, M <= 100000)

In the second line there are N integers. The ith integer denotes the weight of the ith node.

In the next N-1 lines, each line contains two integers u v, which describes an edge (u, v).

In the next M lines, each line contains three integers u v k, which means an operation asking for the kth minimum weight on the path from node u to node v.

Output

For each operation, print its result.

Example

Input:
8 5
105 2 9 3 8 5 7 7
1 2
1 3
1 4
3 5
3 6
3 7
4 8
2 5 1
2 5 2
2 5 3
2 5 4
7 8 2 
Output:
2
8
9
105

hide comments
ankit mathur: 2017-07-17 16:45:20

I found this Tc as the trickest one.
7 7
4 10 2 2 5 5 4
1 2
2 3
3 4
4 5
5 6
6 7
1 7 1
1 7 2
1 7 3
1 7 4
1 7 5
1 7 6
1 7 7
Output:
2
2
4
4
5
5
10

Also weight of nodes could be -ve also. and weight of nodes is greater than 10^5.

kaushik_r: 2017-06-06 14:56:41

If we list the elements in the path from node 7 to node 8 in the given example, we'll get [7, 9, 105, 3, 7] . The 3rd minimum number in the list is 7 or 9?
EDIT: Okay its 7

Last edit: 2017-06-06 15:50:58
r_ash: 2017-05-28 06:18:17

Last edit: 2017-06-03 13:42:35
californiagurl: 2017-05-23 15:24:46

I am getting WA. Is there any tricky test case? I used persistent segment tree, and even used long long.

Last edit: 2017-05-23 15:27:13
chunkitlau: 2017-02-16 09:45:18

Last edit: 2017-02-16 09:49:50
Ravi kumar: 2016-10-26 23:25:44

n & m are greater than 10^5. cost me few wa :(

vsp4: 2016-07-23 11:33:36

Very strict time limit. Had to use fast input output and then compress code :| :| due to source limit exceeding with fast input output -_-

arjundabra: 2016-07-16 12:06:34

getting seg fault in c++ 5.1 but got ac in c++ 4.3.2.Why??

xxbloodysantaxx: 2016-06-16 11:34:31

Submit in 4.3.2 , it runs faster .
Unnecessarily strict time limit..

snow_my_dream: 2016-02-23 14:20:02

I spent ONE day on it. But why I can't Accepted!!!!


Added by:Fotile
Date:2012-02-14
Time limit:1s
Source limit:6000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
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