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 CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
int n, k, vis[200024], sum, maxr, x, y, Ans[200024], cnt;
struct info {
  int l, r, id;
} q[200024];
bool operator<(info A, info B) { return A.r < B.r; }
vector<info> G[200024];
int Read() {
  int num = 0;
  char c = getchar();
  while (c < '0' || c > '9') c = getchar();
  while (c >= '0' && c <= '9')
    num = (num << 3) + (num << 1) + c - 48, c = getchar();
  return num;
}
int main() {
  n = Read(), k = Read();
  for (int i = 1; i <= n; i++) {
    x = Read(), y = Read();
    vis[x]++;
    vis[y + 1]--;
    maxr = max(maxr, y);
    G[x].push_back({x, y, i});
  }
  priority_queue<info> q;
  for (int i = 1; i <= maxr; i++) {
    sum += vis[i];
    for (int j = G[i].size(); j; j--) q.push(G[i][j - 1]);
    while (sum > k) {
      info now = q.top();
      q.pop();
      Ans[++cnt] = now.id;
      sum--;
      vis[now.r + 1]++;
    }
  }
  printf("%d\n", cnt);
  for (int i = 1; i <= cnt; i++) printf("%d ", Ans[i]);
}