Problem Statement

Takahashi is conducting an evacuation simulation inside a building.

The building has N rooms and M corridors. The rooms are numbered from 1 to N, and each corridor bidirectionally connects two distinct rooms. There is at most one corridor connecting any pair of rooms.

There is no limit on the number of people that can pass through corridors or be in rooms. Multiple evacuees can use the same corridor in the same turn, and any number of evacuees can be in the same room without issue. Each evacuee's actions do not affect the others.

There are K evacuees in the building. Evacuee i (1 \leq i \leq K) is initially in room S_i. Different evacuees may be in the same room.

Additionally, fires have broken out in Q rooms of the building. The rooms on fire are P_1, P_2, \ldots, P_Q, all of which are distinct. Fires continue to burn throughout the simulation but do not spread to other rooms.

Room T is the emergency exit, and it is not on fire. All evacuees have complete knowledge of the entire graph structure, fire locations, and positions of other evacuees, and they all act optimally so that everyone can reach room T. Each evacuee can independently choose their action (moving to a different room or staying) within the same turn.

Simulation Progression

The simulation proceeds in turns. Once an evacuee has been eliminated or has completed evacuation, they do not participate in subsequent turns.

Initial Processing (Before Turn 1)

At the start of the simulation, the following processing occurs:

• Evacuees whose initial position is room T immediately complete evacuation.
• Evacuees whose initial position is a room on fire are immediately eliminated and fail to evacuate.

Due to the constraints, room T is never on fire, so no evacuee can satisfy both conditions.

Processing Each Turn

After that, the following processing occurs in each turn in this order:

1. Movement Phase: All evacuees who have neither been eliminated nor completed evacuation act simultaneously. Each evacuee chooses either to move to one adjacent room directly connected to their current room by a corridor, or to stay in their current room. In a single movement phase, an evacuee can move at most one corridor (to one adjacent room).
2. Evacuation Completion Check: Evacuees who are in room T after moving complete evacuation.
3. Elimination Check: Evacuees who are in a room on fire after moving are eliminated. Due to the constraints, room T is never on fire, so an evacuee who completed evacuation in step 2 will not be eliminated in this step.

Note: Moving to a room on fire is not prohibited, but doing so results in elimination during the elimination check. Therefore, since an evacuee can move at most one adjacent room per movement phase, it is impossible to "pass through" a room on fire to reach the other side.

Objective

Determine whether all evacuees can reach room T without being eliminated. If everyone can reach it, find the minimum number of turns required for all evacuees to complete evacuation.

If all evacuees have already completed evacuation at the start of the simulation (i.e., everyone's initial position is room T), the required number of turns is 0.

If even one evacuee cannot avoid elimination, then evacuation of everyone is impossible. In particular, if any evacuee's initial position is a room on fire, they are eliminated at the start, so evacuation is necessarily impossible in such cases.

Constraints

• 1 \leq N \leq 2 \times 10^5
• 0 \leq M \leq 2 \times 10^5
• 1 \leq K \leq 2 \times 10^5
• 0 \leq Q \leq N
• 1 \leq T \leq N
• 1 \leq U_i, V_i \leq N \ (1 \leq i \leq M)
• U_i \neq V_i \ (1 \leq i \leq M)
• There is at most one corridor connecting any pair of rooms
• 1 \leq S_i \leq N \ (1 \leq i \leq K)
• S_i may contain duplicates
• 1 \leq P_j \leq N \ (1 \leq j \leq Q)
• All P_j are distinct
• P_j \neq T for all j
• The graph is not necessarily connected
• An evacuee's initial position may be a room on fire
• All input values are integers

Sample Input 1

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

Sample Output 1

3

Sample Input 2

6 5 3 1 6
1 2
2 3
3 4
4 5
5 6
1 3 5
3

Sample Output 2

-1

Sample Input 3

12 14 6 2 12
1 2
2 3
3 4
4 12
2 5
5 7
7 8
8 12
3 6
9 10
9 11
11 12
5 9
1 7
1 5 9 11 12 7
6 10

Sample Output 3

3

Sample Input 4

20 19 10 4 20
1 2
2 3
3 4
4 5
5 6
6 7
7 8
8 9
9 10
10 11
11 12
12 13
13 14
14 15
15 20
4 16
7 17
10 18
13 19
1 3 5 7 9 11 13 15 20 1
16 17 18 19

Sample Output 4

15

Sample Input 5

1 0 1 0 1
1

Sample Output 5

0