#D1331. Too Many Segments (hard version)
Too Many Segments (hard version)
Too Many Segments (hard version)
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
inputFormat
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.
outputFormat
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
样例
5 1
29 30
30 30
29 29
28 30
30 30
3
4 1 5