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문제

Bessie and Jonell are great friends. Since Farmer John scrambles where the cows graze every day, they are sometimes quite far from each other and can't talk.

The pastures and paths on FJ's farm form a 'tree' structure. Each pasture has exactly one distinct path to any other pasture, and each pasture (except pasture #1, the 'root') also has a single parent node.

Bessie and Jonell have decided that they will always meet at the closest pasture that that is both an ancestor of Jonell's pasture and of Bessie's pasture.

FJ created a map of his N (1 <= N <= 1,000) pastures (conveniently numbered 1..N) that tells the parent P_i (1 <= P_i <= N) of each pasture except pasture 1, which has no parent.

FJ has released his daily grazing schedule for the next M (1 <= M <= 1,000) days, so Bessie and Jonell are deciding where they should meet each day for gossip. On day k, Bessie is in pasture B_k (1 <= B_k <= N) and Jonell is in pasture J_k (1 <= J_k <= N).

Given a map and schedule, help Bessie and Jonell find their meeting places.

Consider, for example, the following farm layout:

                            Pasture      Parent Pasture
             [1]           ---------    ----------------
            / | \              1              ---
           /  |  \             2               1 
         [2] [3] [6]           3               1
         /        | \          4               2
        /         |  \         5               8
      [4]        [8]  [9]      6               1
                /   \          7               8
               /     \         8               6
             [5]     [7]       9               6

Here are the meeting places that Bessie and Jonell would choose given a six day schedule of their initial grazing locations:

              Bessie      Jonell       Meeting Place
             --------    --------     ---------------
                 2           7               1
                 4           2               2
                 1           1               1
                 4           1               1
                 7           5               8
                 9           5               6

입력

  • Line 1: Two space-separated integers: N and M
  • Lines 2..N: Line i contains a single integer that describes the parent of pasture i:  P_i
  • Lines N+1..N+M: Line k+N describes Bessie and Jonell's respective pastures with two space-separated integers: B_k and J_k

 

출력

  • Lines 1..M: Line j contains the meeting place Bessie and Jonell would use for line j+N of the input

 

예제 입력

9 6
1
1
2
8
1
8
6
6
2 7
4 2
3 3
4 1
7 5
9 5

예제 출력

1
2
3
1
8
6

힌트