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>
#pragma GCC optimize("Ofast,unroll-loops,-ffloat-store")
#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,avx2,fma")
using namespace std;
const int m = 2e5;
const int maxn = 2e5 + 5;
int n, k, a[maxn], b[maxn];
vector<pair<int, int> > V[maxn];
vector<int> ans;
void readf() {
  cin >> n >> k;
  for (int i = 1; i <= n; ++i) {
    int l, r;
    cin >> l >> r;
    a[l]++;
    a[r + 1]--;
    V[l].emplace_back(r, i);
  }
  for (int i = 1; i <= m; ++i) a[i] += a[i - 1];
}
void solve() {
  priority_queue<pair<int, int> > pq;
  for (int i = 1; i <= m; ++i) a[i] = max(0, a[i] - k);
  int cnt = 0;
  for (int i = 1; i <= m; ++i) {
    cnt += b[i];
    for (auto it : V[i]) pq.push(it);
    a[i] += cnt;
    while (a[i] > 0 && pq.size() > 0) {
      pair<int, int> tmp = pq.top();
      pq.pop();
      ans.emplace_back(tmp.second);
      cnt--;
      b[tmp.first + 1]++;
      a[i]--;
    }
  }
  cout << ans.size() << '\n';
  for (auto x : ans) cout << x << ' ';
}
int main() {
  srand(time(NULL));
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  readf();
  solve();
}