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 PYTHON):

Solution:
from sys import stdin
from heapq import *

rints = lambda: [int(x) for x in stdin.readline().split()]
Max = 2 * 10 ** 5 + 2

n, m = rints()
a, ans = sorted([rints() + [i] for i in range(1, n + 1)], key=lambda x: (x[0], -x[1]))[::-1], []
plus, minus = [0] * Max, [0] * Max

for i in range(n):
    plus[a[i][0]] += 1
    plus[a[i][1] + 1] -= 1

cur, queue = 0, []
heapify(queue)

for i in range(1, Max):
    cur += plus[i] + minus[i]
    # print(cur)

    while cur > m:
        ma1, ma2 = [0, 0], [0, 0]

        if a and a[-1][0] == i:
            ma1 = [a[-1][1], a[-1][2]]

        if queue and abs(queue[0][0]) > ma1[0]:
            ma2 = queue[0]
            ma2[0] = abs(ma2[0])

        if ma1[0] >= ma2[0]:
            a.pop()
            ans.append(ma1[1])
            minus[ma1[0] + 1] += 1
        else:
            heappop(queue)
            ans.append(ma2[1])
            minus[ma2[0] + 1] += 1

        cur -= 1

    while a:
        if a[-1][0] == i:
            heappush(queue, [-a[-1][1], a[-1][2]])
            a.pop()
        else:
            break

print('%d\n%s' % (len(ans), ' '.join(map(str, ans))))