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;
const long long N = 200005, INF = 2000000000000000000;
long double pi = 3.1415926535897932;
long long power(long long a, long long b, long long p) {
  if (a == 0) return 0;
  long long res = 1;
  a %= p;
  while (b > 0) {
    if (b & 1) res = (res * a) % p;
    b >>= 1;
    a = (a * a) % p;
  }
  return res;
}
long long BIT[N], a[N], n = N;
void update(long long x, long long delta) {
  for (; x <= n; x += x & -x) BIT[x] += delta;
}
long long query(long long x) {
  long long sum = 0;
  for (; x > 0; x -= x & -x) sum += BIT[x];
  return sum;
}
int32_t main() {
  std::ios::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  cout.precision(std::numeric_limits<double>::max_digits10);
  ;
  long long s, ans = 0, k;
  cin >> s >> k;
  vector<long long> fans;
  vector<tuple<long long, long long, long long> > v;
  for (long long i = 0; i < s; i++) {
    long long l, r;
    cin >> l >> r;
    update(l, 1);
    update(r + 1, -1);
    v.push_back({l, r, i + 1});
  }
  sort((v).begin(), (v).end());
  long long x = 0;
  map<tuple<long long, long long, long long>, long long> mp;
  for (long long i = 1; i <= 200000; i++) {
    while (x < s) {
      long long p, q, r;
      tie(p, q, r) = v[x];
      if (p <= i) {
        mp[{q, p, r}]++;
        x++;
      } else
        break;
    }
    while (query(i) > k) {
      auto it = mp.end();
      it--;
      long long p, q, r;
      tie(p, q, r) = (*it).first;
      ans++;
      fans.push_back(r);
      update(q, -1);
      update(p + 1, 1);
      mp.erase((*it).first);
    }
  }
  cout << ans << "\n";
  for (long long i = 0; i < ans; i++) cout << fans[i] << " ";
}