Optimal Pasture Sleep Location

Bessie wants to minimize the average travel time from her sleeping pasture to all of her favorite pastures. Farmer John's farm is composed of P pastures (numbered 1 to P), connected by C bidirectional cowpaths. Bessie has F favorite pastures. Each cowpath connects two pastures and takes T units of time to traverse.

Formally, let d(x, y) be the shortest distance between pastures x and y. For a candidate pasture x, the average time to reach all favorites is given by:

\(\frac{\sum_{f \in Favorites} d(x, f)}{F}\)

Your task is to choose the pasture from which this average is minimized. In the event of a tie (i.e. multiple pastures yield the same average travel time), choose the one with the smallest numerical label.

Note: It is guaranteed that all pastures are connected (i.e. it is possible to reach any pasture from any other pasture).

inputFormat

Input Format:

• The first line contains three integers: P, F, and C where  1 ≤ P ≤ 500, 1 ≤ F ≤ P, and 1 < C ≤ 8000.
• The second line contains F integers representing the favorite pastures.
• Each of the next C lines contains three integers: a, b, and T (with 1 ≤ T < 892), indicating a bidirectional cowpath connecting pastures a and b that takes T time units to traverse.

outputFormat

Output Format:

Print a single integer: the number of the pasture that minimizes the average travel time to all favorite pastures. If multiple pastures yield the same minimum average time, output the smallest numbered pasture.

sample

5 2 4
2 4
1 2 2
1 3 1
1 4 3
1 5 4

1