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:
from heapq import *


def main():
    n, k = map(int, input().split())
    E = []
    opent = {}
    for i in range(n):
        l, r = map(int, input().split())
        E.append([l, 1, i])
        E.append([r, -1, i])
        opent[i] = r
    E.sort(key=lambda x: (x[0], -x[1]))
    now_r = []
    heapify(now_r)
    cnt_delet = 0
    ans = []
    deleted = set()
    for x, t, i in E:
        if t == 1:
            heappush(now_r, -(opent[i] * 10 ** 6 + i))
        else:
            if i not in deleted:
                cnt_delet += 1
        if len(now_r) - cnt_delet > k:
            for _ in range(len(now_r) - cnt_delet - k):
                nm = heappop(now_r)
                ind = (-nm) % 10 ** 6
                ans.append(ind + 1)
                deleted.add(ind)
    print(len(ans))
    print(' '.join(list(map(str, ans))))


main()