A13042 | 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 $[l_i; r_i]$ ( $l_i \le r_i$ ) and it covers all integer points $j$ such that $l_i \le j \le r_i$ .

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.

The first line of the input contains two integers $n$ and $k$ ( $1 \le k \le n \le 2 \cdot 10^5$ ) — 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 $r_i$ ( $1 \le l_i \le r_i \le 2 \cdot 10^5$ ) — the endpoints of the $i$ -th segment.

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

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