시간 제한메모리 제한제출정답맞힌 사람정답 비율
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## 문제

Bessie, always wishing to optimize her life, has realized that she really enjoys visiting F (1 <= F <= P) favorite pastures F_i of the P (1 <= P <= 500; 1 <= F_i <= P) total pastures (conveniently numbered 1..P) that compose Farmer John's holdings.

Bessie knows that she can navigate the C (1 <= C <= 8,000) bidirectional cowpaths (conveniently numbered 1..C) that connect various pastures to travel to any pasture on the entire farm. Associated with each path P_i is a time T_i (1 <= T_i <= 892) to traverse that path (in either direction) and two path endpoints a_i and b_i (1 <= a_i <= P; 1 <= b_i <= P).

Bessie wants to find the number of the best pasture to sleep in so that when she awakes, the average time to travel to any of her F favorite pastures is minimized.

By way of example, consider a farm laid out as the map below shows, where *'d pasture numbers are favorites. The bracketed numbers are times to traverse the cowpaths.

            1*--[4]--2--[2]--3
|       |
[3]     [4]
|       |
4--[3]--5--[1]---6---[6]---7--[7]--8*
|       |        |         |
[3]     [2]      [1]       [3]
|       |        |         |
13*      9--[3]--10*--[1]--11*--[3]--12*


The following table shows distances for potential 'best place' of pastures 4, 5, 6, 7, 9, 10, 11, and 12:

                       * * * * * * Favorites * * * * * *
Potential      Pasture Pasture Pasture Pasture Pasture Pasture     Average
Best Pasture       1       8      10      11      12      13        Distance
------------      --      --      --      --      --      --      -----------
4              7      16       5       6       9       3      46/6 = 7.67
5             10      13       2       3       6       6      40/6 = 6.67
6             11      12       1       2       5       7      38/6 = 6.33
7             16       7       4       3       6      12      48/6 = 8.00
9             12      14       3       4       7       8      48/6 = 8.00
10             12      11       0       1       4       8      36/6 = 6.00 ** BEST
11             13      10       1       0       3       9      36/6 = 6.00
12             16      13       4       3       0      12      48/6 = 8.00


Thus, presuming these choices were the best ones (a program would have to check all of them somehow), the best place to sleep is pasture 10.

## 입력

• Line 1: Three space-separated integers: P, F, and C
• Lines 2..F+1: Line i+2 contains a single integer: F_i
• Lines F+2..C+F+1: Line i+F+1 describes cowpath i with three space-separated integers: a_i, b_i, and T_i

## 출력

• Line 1: A single line with a single integer that is the best pasture in which to sleep. If more than one pasture is best, choose the smallest one.

## 예제 입력 1

13 6 15
11
13
10
12
8
1
2 4 3
7 11 3
10 11 1
4 13 3
9 10 3
2 3 2
3 5 4
5 9 2
6 7 6
5 6 1
1 2 4
4 5 3
11 12 3
6 10 1
7 8 7


## 예제 출력 1

10