Problem: The only difference between easy and hard versions is constraints.

You are given n segments on the coordinate axis OX. Segments can intersect, lie inside each other and even coincide. The i-th segment is [l_i; r_i] (l_i ≤ r_i) and it covers all integer points j such that l_i ≤ j ≤ r_i.

The integer point is called bad if it is covered by strictly more than k segments.

Your task is to remove the minimum number of segments so that there are no bad points at all.

Input

The first line of the input contains two integers n and k (1 ≤ k ≤ n ≤ 2 ⋅ 10^5) — the number of segments and the maximum number of segments by which each integer point can be covered.

The next n lines contain segments. The i-th line contains two integers l_i and r_i (1 ≤ l_i ≤ r_i ≤ 2 ⋅ 10^5) — the endpoints of the i-th segment.

Output

In the first line print one integer m (0 ≤ m ≤ n) — the minimum number of segments you need to remove so that there are no bad points.

In the second line print m distinct integers p_1, p_2, ..., p_m (1 ≤ p_i ≤ n) — indices of segments you remove in any order. If there are multiple answers, you can print any of them.

Examples

Input


7 2
11 11
9 11
7 8
8 9
7 8
9 11
7 9


Output


3
4 6 7 


Input


5 1
29 30
30 30
29 29
28 30
30 30


Output


3
1 4 5 


Input


6 1
2 3
3 3
2 3
2 2
2 3
2 3


Output


4
1 3 5 6 

Solution (in PYTHON3):

Solution:
# -*- coding: utf-8 -*-

import sys
import bisect
import heapq

line_count = 0
segments = [None]
num_points = 200000
for line in sys.stdin.readlines():
    inputs = line.split()
    if line_count == 0:
        n = int(inputs[0])
        k = int(inputs[1])
        opening = {}
        closing = {}
        removed_right = {}
        segment_index = 0
        for i in range(1, num_points + 1):
            opening[i] = []
            closing[i] = []
            removed_right[i] = 0
    else:
        l = int(inputs[0])
        r = int(inputs[1])
        segment_index += 1
        segments.append((l, r))
        opening[l].append(segment_index)
        closing[r].append(segment_index)
    if line_count == n:
        break
    line_count += 1

working = []
working_count = 0
removed = []
for i in range(1, num_points + 1):
    for segment_index in opening[i]:
        _, r = segments[segment_index]
        heapq.heappush(working, (- r, segment_index))
        working_count += 1
#        bisect.insort_right(working, (r, segment_index))
    while working_count > k:
        r, segment_index = heapq.heappop(working)
#        r, segment_index = working.pop()
        working_count -= 1
        removed.append(segment_index)
        removed_right[- r] += 1
    squeezed_out = len(closing[i]) - removed_right[i]
    working_count -= squeezed_out
#    working = working[squeezed_out: ]

print(len(removed))
for j in removed:
    print(j, end = " ")