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

$1\le N\le 2\times {10}^3$

$1\le S\le N$

$N\equiv 0(\mathrm{mod}S)$

$1\le K\le S$

$1\le a,b\le N$

$R\in \{$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 $2$.