6085번 - Best Spot 다국어

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.

제한

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