human
Easy and hard versions are actually different problems, so read statements of both problems completely and carefully.

Summer vacation has started so Alice and Bob want to play and joy, but... Their mom doesn't think so. She says that they have to read exactly m books before all entertainments. Alice and Bob will read each book together to end this exercise faster.

There are n books in the family library. The i-th book is described by three integers: t_i — the amount of time Alice and Bob need to spend to read it, a_i (equals 1 if Alice likes the i-th book and 0 if not), and b_i (equals 1 if Bob likes the i-th book and 0 if not).

So they need to choose exactly m books from the given n books in such a way that:

  * Alice likes at least k books from the chosen set and Bob likes at least k books from the chosen set.

  * the total reading time of these m books is minimized (they are children and want to play and joy as soon a possible). 


The set they choose is the same for both Alice an Bob (it's shared between them) and they read all books together, so the total reading time is the sum of t_i over all books that are in the chosen set.

Your task is to help them and find any suitable set of books or determine that it is impossible to find such a set.

Input

The first line of the input contains three integers n, m and k (1 ≤ k ≤ m ≤ n ≤ 2 ⋅ 10^5).

The next n lines contain descriptions of books, one description per line: the i-th line contains three integers t_i, a_i and b_i (1 ≤ t_i ≤ 10^4, 0 ≤ a_i, b_i ≤ 1), where:

  * t_i — the amount of time required for reading the i-th book.

  * a_i equals 1 if Alice likes the i-th book and 0 otherwise.

  * b_i equals 1 if Bob likes the i-th book and 0 otherwise. 

Output

If there is no solution, print only one integer -1.

If the solution exists, print T in the first line — the minimum total reading time of the suitable set of books. In the second line print m distinct integers from 1 to n in any order — indices of books which are in the set you found.

If there...
assistant
#Here is Python program to find any suitable set of books or determine that it is impossible to find such a set.

# SortedList copied from: https://github.com/grantjenks/python-sortedcontainers/blob/master/sortedcontainers/sortedlist.py
# Minified with pyminifier to fit codeforce char limit
from __future__ import print_function
import sys
import traceback
from bisect import bisect_left, bisect_right, insort
from itertools import chain, repeat, starmap
from math import log
from operator import add, eq, ne, gt, ge, lt, le, iadd
from textwrap import dedent

try:
    from collections.abc import Sequence, MutableSequence
except ImportError:
    from collections import Sequence, MutableSequence
from functools import wraps
from sys import hexversion

if hexversion < 0x03000000:
    from itertools import imap as map
    from itertools import izip as zip

    try:
        from thread import get_ident
    except ImportError:
        from dummy_thread import get_ident
else:
    from functools import reduce

    try:
        from _thread import get_ident
    except ImportError:
        from _dummy_thread import get_ident

def recursive_repr(fillvalue="..."):
    def decorating_function(user_function):
        repr_running = set()

        @wraps(user_function)
        def wrapper(self):
            key = id(self), get_ident()
            if key in repr_running:
                return fillvalue
            repr_running.add(key)
            try:
                result = user_function(self)
            finally:
                repr_running.discard(key)
            return result

        return wrapper

    return decorating_function

class SortedList(MutableSequence):
    DEFAULT_LOAD_FACTOR = 1000

    def __init__(self, iterable=None, key=None):
        assert key is None
        self._len = 0
        self._load = self.DEFAULT_LOAD_FACTOR
        self._lists = []
        self._maxes = []
        self._index = []
        self._offset = 0
        if iterable is not None:
            self._update(iterable)

    def __new__(cls, iterable=None, key=None):
        if key is None:
            return object.__new__(cls)
        else:
     ...