A thief is trying to escape the holds of the police through a city. Let’s assume we represent our city by a weighted undirected connected graph(with no self-loops and multi-edges) with N nodes and M edges.

 

Thief is currently at vertex numbered S and needs to reach vertex numbered D. Thief moves with constant speed V_T = 1.

 

K policemen are initially located in K distinct locations denoted by A₁, A₂, ... A_K. Each policeman has a constant speed of V_P = 1.
To help policemen, a single power booster have been provided to them. This power booster can be availed once from any one of the Q distinct ‘special’ nodes B₁, B₂, ... B_Q. Property of this power booster being that it doubles the speed of the policeman who avails this power booster.
Note:
A policeman can choose not to avail the power booster even if he is at a ‘special’ node.
You have to print the shortest time in which thief can escape the police regardless of whatever path the police might take.
If he can’t reach the destination, output -1.

 

 

 

Input

 

First line contains N and M, the number of nodes and number of edges respectively.
Each of the next M lines contain integers u v and w denoting an undirected edge between nodes numbered u and v, w being the weight of the edge.
Next line contains a single integer K denoting number of different policemen. Next line contains K space separated integers denoting the distinct locations A₁, A₂, ... A_K.
Next line contains a single integer Q denoting number of ‘special’ nodes. Next line contains Q distinct space separated integers denoting the locations B₁, B₂, ... B_Q.
Next line contains two distinct integers S and D denoting the source and destination of the thief.

 

Output

 

For each test case print the minimum time required for thief to escape(if possible). Else, output -1.

 

Constraints

 

• 1 = N = 10⁵
• M = min(2 * 10⁵, N*(N-1)/2)
• 0 = u, v, S, D, A_i, B_i
• 0 = K, Q = N
• 1 = w = 10⁹

 

 

Example

Input1: 4 4 0 1 2 1 2 4 2 3 10 3 0 2 1 3 1 0 2 1 Output1: -1

 

Input2: 4 3 0 1 2 1 2 8 1 3 10 2 2 3 2 2 3 0 1 Output2: 2

 

Explanation

Example1:
Police takes the path 3 -> 0 -> 1 availing the power booster at node 0. Even though both policeman and thief reach the destination at same time, police catches thief.
Example2:
Whichever policeman uses the power booster, thief will be able to escape in 2 seconds.