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:
import sys
input = sys.stdin.readline

n,k=map(int,input().split())

S=[tuple(map(int,input().split()))+(i+1,) for i in range(n)]
S.sort()

segtemp=2*10**5
seg_el=1<<((segtemp).bit_length())# Segment treeの台の要素数
SEG=[0]*(2*seg_el)# 1-indexedなので、要素数2*seg_el.Segment treeの初期値で初期化

def getvalue(n,seg_el):# 一点の値を取得
    i=n+seg_el
    ANS=0
    
    ANS+=SEG[i]
    i>>=1# 子ノードへ
    
    while i!=0:
        ANS+=SEG[i]
        i>>=1

    return ANS

def updates(l,r,x):# 区間[l,r)のminを更新.
    L=l+seg_el
    R=r+seg_el

    while L<R:
        if L & 1:
            SEG[L]+=x
            L+=1

        if R & 1:
            R-=1
            SEG[R]+=x
        L>>=1
        R>>=1

ind=0
SH=[]
ANS=[]
import heapq

for point in range(segtemp):
    while ind<n and S[ind][0]<=point:
        l,r,x=S[ind]
        updates(l,r+1,1)
        ind+=1

        heapq.heappush(SH,(-r,l,x))

    #print(getvalue(point,seg_el),SH)

    while getvalue(point,seg_el)>k:
        r,l,x=heapq.heappop(SH)
        r=-r
        ANS.append(x)
        updates(l,r+1,-1)

    #print(point,ANS,getvalue(point,seg_el))
        
print(len(ANS))
print(*ANS)