The hockey event at the Winter Olympics will be happening soon! UselessLeaf will bet with his friends about how the countries will place.

The tournament will be operating in a round-robin fashion. There are ~N~ countries competing, numbered from ~1~ to ~N~, and they will be split into groups of size ~S~. ~\frac{S(S-1)}{2}~ matches will then occur in each group, where each country in their group play against each other country in the group once, resulting in a total of ~\frac{(S-1)N}{2}~ matches. After a match, the winning country gains 3 points, while the losing country gains 0. If it is a tie, both countries gain 1 point.

The tournament ends when all ~\frac{S(S-1)}{2} \times \frac{N}{S} = \frac{(S-1)N}{2}~ matches have been played. The countries in each group will then be ranked by their points. If there is a tie, the lower-numbered country should be ranked better (for example, if country ~i~ and country ~j~ where ~i < j~ got the same number of points, country ~i~ should be ranked better than country ~j~).

A time traveller has suddenly appeared and provided UselessLeaf with the results of the ~\frac{(S-1)N}{2}~ matches. He provides the two countries in the match, ~a~ and ~b~, and the result of the match, an uppercase letter ~R~ where W means country ~a~ won the match, L means country ~b~ won the match, and T means the match ended in a tie.

UselessLeaf is participating in a bet where he has to guess the country that places ~K^\text{th}~ in each group and needs your help figuring this out!

Constraints

~1 \le N \le 2 \times 10^3~

~1 \le S \le N~

~N \equiv 0 \pmod{S}~

~1 \le K \le S~

~1 \le a, b \le N~

~R \in \{~W~,~L~,~T~\}~

Subtask 1 [5/15]

~S = N~

Subtask 2 [10/15]

No additional constraints.

Input Specification

The first line will contain two space-separated integers ~N~, the number of countries competing, and ~S~, the number of countries in each group.

The next ~\frac{N}{S}~ lines will contain ~S~ space-separated integers, the ~i^\text{th}~ line containing the countries that are in the ~i^\text{th}~ group.

The next ~\frac{(S-1)N}{2}~ lines will contain two space-separated integers ~a~ and ~b~, the countries involved in this match, and one character ~R~, the result of the match between country ~a~ and country ~b~.

The next line will contain one integer ~K~, where UselessLeaf must figure out which country placed ~K^\text{th}~ in each group.

Output Specification

Output ~\frac{N}{S}~ space-separated integers, the ~i^\text{th}~ integer being the country that placed ~K^\text{th}~ in the ~i^\text{th}~ group.

Sample Input

4 2
3 1
2 4
1 3 W
2 4 T
2

Sample Output

3 4

Explanation

In group ~1~, since 1 beat 3, 1 is ranked ~1~, while 3 is ranked ~2~. In group ~2~, there is a tie for first and second in terms of points between 2 and 4, but 2 is the lower numbered country so is ranked ~1~, meaning 4 is ranked ~2~.