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 PYTHON3):

Solution:
'''
template author-: Pyduper
'''
import sys

# stdin = open("testdata.txt", "r")
# ip = stdin
# def input():
# 	return ip.readline().strip()

def input():
	return sys.stdin.readline().strip()

import heapq
maxn = 200005
def lowbit(x):
	return x&-x
def add(t,i,v):
	while i<len(t):
		t[i]+=v
		i += lowbit(i)
def sum(t,i):
	ans = 0
	while i>0:
		ans += t[i]
		i -= lowbit(i)
	return ans
trees = [0]*maxn
 
n,k = map(int,input().split(" "))
seg = []
points = [0]*maxn
cand = []
for i in range(n):
	l,r = map(int,input().split(" "))
	seg.append((l,r,i+1))
	points[l]   += 1
	points[r+1] -= 1
st = 0
for i in range(maxn):
	st += points[i]
	if st > k:
		cand.append((i,st-k))
 
seg.sort(key = lambda x:(x[0],x[1]))
pq = []
j = 0
ans = []
for i,v in cand:
	v = v-sum(trees,i)
	if v <= 0:
		continue
	while j<n and seg[j][0] <= i:
		heapq.heappush(pq,(-seg[j][1],seg[j][0],seg[j][2]))
		j += 1
 
	for t in range(v):
		r,l,idx = heapq.heappop(pq)
		ans.append(idx)
		add(trees,l,1)
		add(trees,-r+1,-1)
 
print(len(ans))
print(*ans)