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, heapq
mmx = 200000
ftree = [0]*(mmx+1)
def uu(i, j, v):
    while i <= mmx:
        ftree[i] += v
        i += (i&-i)
    j += 1
    while j <= mmx:
        ftree[j] -= v
        j += (j&-j)
def qq(j):
    s = 0
    while j > 0:
        s += ftree[j]
        j -= (j & -j)
    return s
n, k = [int(i) for i in sys.stdin.readline().split()]
lns = sys.stdin.readlines()
bds = []
for j in range(n):
    t = [int(i) for i in lns[j].split()]
    t.append(j+1)
    bds.append(t)
    uu(bds[-1][0], bds[-1][1], 1)
bds.sort()
bind = 0
heap = []
ans = []
for i in range(1, mmx+1):
    while bind < n and bds[bind][0] == i:
        heapq.heappush(heap, (-1*bds[bind][1], bds[bind][2]))
        bind += 1
    while qq(i) > k:
        bd, bnd = heapq.heappop(heap) 
        ans.append(str(bnd))
        uu(i,-1*bd, -1)
print(len(ans))
print(" ".join(ans))