Summit Partner Gear Endorsements

A mountaineering club tracks climbing partnerships and gear endorsements. Partnerships are mutual: whenever climber a and climber b are recorded as partners, each is considered a partner of the other, and no climber is ever listed as their own partner. Separately, an endorsement record states that a specific climber endorses a specific piece of gear; a climber may endorse several different items, and no climber-gear pair carries any special meaning beyond "this climber endorses this gear."

Given the full partnership list, the full endorsement list, and the id of one target climber, find every distinct gear id that at least one of the target climber's partners endorses, except for any gear id the target climber already endorses themself. If the target climber has no recorded partners, there is nothing to recommend.

Input format

The first line contains three integers p, l, and x -- the number of partnership records, the number of endorsement records, and the target climber's id, respectively. Each of the next p lines contains two integers a b, meaning climbers a and b are partners (a != b). Each of the next l lines contains two integers u g, meaning climber u endorses gear item g.

Output format

Print the recommended gear ids, each on its own line, in strictly increasing order and with no duplicates. If there are no recommendations, print nothing.

Constraints

• 1 <= p <= 2*10^4
• 1 <= l <= 5*10^4
• 1 <= a, b, u, g, x <= 10^5
• a != b for every partnership record
• A given unordered pair of climbers may repeat across multiple partnership records, and a given (u, g) endorsement may also repeat; your answer must be unaffected by such repeats.

3 4 1
1 2
1 3
2 4
1 88
2 23
3 24
4 56

23
24

2 5 5
5 6
5 7
5 10
6 10
6 11
7 11
7 12

11
12