The competitors of Bubble Cup X gathered after the competition and discussed what is the best way to get to know the host country and its cities. After exploring the map of Serbia for a while, the competitors came up with the following facts: the country has V cities which are indexed with numbers from 1 to V , and there are E bi-directional roads that connect the cites. Each road has a weight (the time needed to cross that road). There are N teams at the Bubble Cup and the competitors came up with the following plan: each of the N teams will start their journey in one of the V cities, and some of the teams share the starting position. They want to find the shortest time T , such that every team can move in these T minutes, and the number of different cities they end up in is at least K (because they will only get to know the cities they end up in). A team doesn't have to be on the move all the time, if they like it in a particular city, they can stay there and wait for the time to pass. Please help the competitors to determine the shortest time T so it's possible for them to end up in at least K different cities or print -1 if that is impossible no matter how they move. Note that there can exist multiple roads between some cities. The first line contains four integers: V , E , N and K (1 ≤ V ≤ 600, 1 ≤ E ≤ 20000, 1 ≤ N ≤ min ( V , 200), 1 ≤ K ≤ N ) , number of cities, number of roads, number of teams and the smallest number of different cities they need to end up in, respectively. The second line contains N integers, the cities where the teams start their journey. Next E lines contain information about the roads in following format: A i B i T i (1 ≤ A i , B i ≤ V , 1 ≤ T i ≤ 10000) , which means that there is a road connecting cities A i and B i , and you need T i minutes to cross that road. Output a single integer that represents the minimal time the teams can move for, such that they end up in at least K different cities or output -1 if there is no solu