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 optimize("TKACHENKO-GORYACHENKO")
#pragma GCC optimize("O3")
using namespace std;
const long long maxn = 3e5 + 10;
long long n, m, k;
long long st3[maxn];
struct seg {
  long long l;
  long long r;
  long long i;
};
bool operator<(seg a, seg b) {
  if (a.r == b.r) {
    return a.i < b.i;
  }
  return a.r > b.r;
}
seg A[maxn];
vector<seg> L[maxn];
vector<seg> R[maxn];
set<seg> S;
vector<long long> ANS;
signed main() {
  long long q, w, e, a, b, c;
  cin >> n >> k;
  for (q = 0; q < n; q++) {
    cin >> A[q].l >> A[q].r;
    A[q].i = q;
    L[A[q].l].push_back(A[q]);
    R[A[q].r].push_back(A[q]);
  }
  for (q = 0; q < maxn; q++) {
    for (w = 0; w < L[q].size(); w++) {
      S.insert(L[q][w]);
    }
    while (S.size() > k) {
      seg del = *(S.begin());
      ANS.push_back(del.i);
      S.erase(S.begin());
    }
    for (w = 0; w < R[q].size(); w++) {
      S.erase(R[q][w]);
    }
  }
  cout << ANS.size() << endl;
  for (q = 0; q < ANS.size(); q++) {
    cout << ANS[q] + 1 << " ";
  }
}