Problem Statement

A total of $N$ teams participated in the ICPC Domestic Qualifier. The $N$ teams are numbered $0, 1, ..., N-1$.

For each team, you are given the following information: the number of problems solved, the penalty, and which university the team belongs to. $K$ teams can advance past the Domestic Qualifier. These $K$ teams are determined one team at a time, based on the above information, using the following algorithm.

1. Among the teams not yet selected, select the team that solved the most problems.
2. If there are multiple teams not yet selected that solved the most problems, select the team with the smaller "number of teams from the same university selected so far".
3. If there are multiple teams not yet selected with the same number of problems solved and the same "number of teams from the same university selected so far", select the team with the smaller penalty.

Your task is to determine, from this information, which teams advanced past the Domestic Qualifier.

Input

$N$ $K$
$S_1$ $P_1$ $U_1$
$S_2$ $P_2$ $U_2$
...
$S_N$ $P_N$ $U_N$

The first line gives the number of participating teams $N$ and the number of teams to be selected $K$.
$1 \leq N \leq 10^5$, $1 \leq K \leq N$
The following $N$ lines give the information for each team. $S_i$ is the number of problems solved by the $i$-th team, $P_i$ is the penalty of the $i$-th team, and $U_i$ is a numerical representation of the university of the $i$-th team.
$0 \leq S_i \leq 10$, $0 \leq P_i \leq 10^6, 1 \leq U_i \leq 10^5$
$P_i, U_i$ are integers
For any two distinct integers $i, j$, the pairs $(S_i, P_i)$ and $(S_j, P_j)$ are never identical

Output

Output the selected $K$ teams, 0-indexed, one per line. The $K$ teams must be output in the order in which they were selected (see the samples for details). Print a newline at the end.

Sample

5 3
3 100 1
4 200 1
4 300 1
3 150 2
2 50 2

1
2
3

3 2
4 100 1
5 300 2
3 100 2

1
0