Problem:
Score : 600 points

Problem Statement

There is a grid of squares with H+1 horizontal rows and W vertical columns.

You will start at one of the squares in the top row and repeat moving one square right or down. However, for each integer i from 1 through H, you cannot move down from the A_i-th, (A_i + 1)-th, \ldots, B_i-th squares from the left in the i-th row from the top.

For each integer k from 1 through H, find the minimum number of moves needed to reach one of the squares in the (k+1)-th row from the top. (The starting square can be chosen individually for each case.) If, starting from any square in the top row, none of the squares in the (k+1)-th row can be reached, print -1 instead.

Constraints

1 \leq H,W \leq 2\times 10^5

1 \leq A_i \leq B_i \leq W

Input

Input is given from Standard Input in the following format:

H W
A_1 B_1
A_2 B_2
:
A_H B_H

Output

Print H lines. The i-th line should contain the answer for the case k=i.

Sample Input 1

4 4
2 4
1 1
2 3
2 4

Sample Output 1

1
3
6
-1

Let (i,j) denote the square at the i-th row from the top and j-th column from the left.

For k=1, we need one move such as (1,1) → (2,1).

For k=2, we need three moves such as (1,1) → (2,1) → (2,2) → (3,2).

For k=3, we need six moves such as (1,1) → (2,1) → (2,2) → (3,2) → (3,3) → (3,4) → (4,4).

For k=4, it is impossible to reach any square in the fifth row from the top.

Solution in C++ (GCC 9.2.1) (judge verdict: Runtime Error)

#include <bits/stdc++.h>
#define maxn 200086

using namespace std;

int n, m;

struct Node{
	bool cov;
	int l, r;
}t[maxn << 2];

#define ls(x) (x << 1)
#define rs(x) (x << 1 | 1)

inline void up(int x){
	if(t[x].cov) t[x].l = n + 1, t[x].r = 0;
	else t[x].r = max(t[ls(x)].r, t[rs(x)].r), t[x].l = min(t[ls(x)].l, t[rs(x)].l);
}

void modify(int x, int l, int r, int ll, int rr){
	if(t[x].cov) return;
	if(ll <= l && r <= rr){
		t[x].cov = true, up(x);
		return;
	}
	int mid = l + r >> 1;
	if(mid >= ll) modify(ls(x), l, mid, ll, rr);
	if(mid < rr) modify(rs(x), mid + 1, r, ll, rr);
	up(x);
}

void build(int x, int l, int r){
	t[x].cov = false;
	if(l == r){
		t[x].l = t[x].r = l;
		return;
	}
	int mid = l + r >> 1;
	build(ls(x), l, mid), build(rs(x), mid + 1, r);
	up(x);
}



int x, y, l, r;
int sum;
bool tag;

int main(){
	scanf("%d%d", &n, &m);
	l = 1, r = m;
	build(1, l, r);
	for(int i = 1;i <= n;i++){
		scanf("%d%d", &x, &y);
		if(tag){
			puts("-1");
			continue;
		}
		int j = t[1].r;
		modify(1, l, r, x, y);
		if(!t[1].r){
			if(y == m){
				puts("-1");
				tag = true;
				continue;
			}
			sum += y + 1 - j;
			l = y + 1, r = n;
			build(1, l, r);
		}
		printf("%d\n", sum + i + (l == 1 ? 0 : (t[1].l - l)));
	}
}