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;
struct node {
  int ind, y;
};
bool operator<(node a, node b) {
  if (a.y != b.y) return a.y < b.y;
  return a.ind < b.ind;
}
vector<node> ve[200000 + 10];
vector<int> ans;
int main() {
  int x, y, k, n;
  cin >> n >> k;
  for (int i = 1; i <= n; i++) {
    cin >> x >> y;
    node nd = {i, y};
    ve[x].push_back(nd);
  }
  set<node> st;
  for (int i = 1; i <= 200000; i++) {
    while (st.size() && (*st.begin()).y < i) st.erase(st.begin());
    for (auto it : ve[i]) st.insert(it);
    while (st.size() > k) {
      ans.push_back((*st.rbegin()).ind);
      st.erase(*(st.rbegin()));
    }
  }
  cout << ans.size() << endl;
  for (auto it : ans) cout << it << " ";
  cout << endl;
}