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 JAVA):

Solution:
'use strict'

class SegmentTree {
    constructor(a, op, init) {
        this.init = init;
        this.op = op;
        this.n = 1 << Math.ceil(Math.log2(a.length));
        this.t = Array(2 * this.n).fill(init);
    }

    update(i, x) {
        for (this.t[i + this.n] = [ x, i ], i += this.n; i > 1; i >>= 1) {
            this.t[i >> 1] = this.op(this.t[i], this.t[i^1]);
        }
    }
}

const NK = readline().split(' ').map(Number);
const N = NK[0];
const K = NK[1];

const LRs = [];
const R = Array.from({ length: N + 1 }, () => 0);

for (let i = 1; i <= N; i++) {
    const lr = readline().split(' ');
    const l = +lr[0];
    let r = +lr[1];
    R[i] = r++;
    if (LRs[l]) LRs[l].push(i); else LRs[l] = [ i ];
    if (LRs[r]) LRs[r].push(-i); else LRs[r] = [ -i ];
}

const sti = new SegmentTree(R, (a, b) => (a[0] < b[0]) ? b : a, [ 0, 0 ]);

let k = 0;
let ans = [];
let removed = new Set();

LRs.filter(Array.isArray).forEach(lrs => {
    lrs.forEach(i => {
        if (i > 0) {
            sti.update(i, R[i]);
            return k++;
        }
        if(!removed.has(-i)) {
            sti.update(-i, 0);
            return k--;
        }
    })
    for(; k > K; k--) {
        const i = sti.t[1][1];
        sti.update(i, 0);
        ans.push(i);
        removed.add(i);
    }
})

print(ans.length);
print(ans.join(' '));