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;
void fastInOut();
const int N = 2e5 + 5;
vector<int> st[N], ed[N];
pair<int, int> segs[N];
int main() {
  fastInOut();
  int n, k;
  cin >> n >> k;
  for (int i = 0; i < n; ++i) {
    cin >> segs[i].first >> segs[i].second;
    st[segs[i].first].push_back(i);
    ed[segs[i].second].push_back(i);
  }
  set<pair<int, int> > S;
  vector<int> ans;
  for (int i = 0; i < N; ++i) {
    for (int seg : st[i]) S.insert({segs[seg].second, seg});
    while (S.size() > k) {
      auto it = prev(S.end());
      ans.push_back(it->second);
      S.erase(it);
    }
    for (int seg : ed[i]) S.erase({segs[seg].second, seg});
  }
  cout << (int)ans.size() << '\n';
  for (int i : ans) cout << i + 1 << ' ';
  cout << '\n';
  return 0;
}
void fastInOut() {
  ios_base::sync_with_stdio(0);
  cin.tie(NULL), cout.tie(NULL);
}