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# (Mono-mcs 6.8.0.105) (judge verdict: Time Limit Exceeded)

using System;
using System.Collections.Generic;
class Program
{
	static void Main(string[] args)
	{
		string[] str = Console.ReadLine().Split();
		int H = int.Parse(str[0]);
		int W = int.Parse(str[1]);
		int[,]A = new int[H,2];
		for(var i=0;i<H;i++){
			string[] str2 = Console.ReadLine().Split();
			A[i,0] = int.Parse(str2[0])-1;
			A[i,1] = int.Parse(str2[1])-1;
		}
		var list = new List<int[]>();
		list.Add(new int[3]{0,W,0});
		for(var i=0;i<H;i++){
			var list2 = new List<int[]>(list);
			list.Clear();
			int k = 999999999;
			for(var j=0;j<list2.Count;j++){
				if(list2[j][1] < A[i,0] || list2[j][0] > A[i,1]){
					list.Add(new int[3]{list2[j][0],list2[j][1],list2[j][2]+1});
				} else if(list2[j][0] < A[i,0]){
					list.Add(new int[3]{list2[j][0],A[i,0]-1,list2[j][2]+1});
					if(A[i,1] < W-1){
						if(list2[j][1] <= A[i,1]){
 							k = Math.Min(k,A[i,1]-list2[j][1]+list2[j][2]+2);
						} else {
							list.Add(new int[3]{A[i,1]+1,list2[j][1],list2[j][2]+1});
						}
					}
				} else if(list2[j][1] <= A[i,1]){
					if(A[i,1] < W-1){
						k = Math.Min(k,A[i,1]-list2[j][1]+list2[j][2]+2);
					}
				} else {
					if(A[i,1] < W-1){
						list.Add(new int[3]{A[i,1]+1,list2[j][1],Math.Min(k,list2[j][2]+1)});
					}
					k = 999999999;
				}
			}
			if(k < 999999999){
				if(A[i,1] < W-1){
					list.Add(new int[3]{A[i,1]+1,A[i,1]+1,k});
				}
			}
			long ans = 999999999;
			for(var j=0;j<list.Count;j++){
				ans = Math.Min(ans,list[j][2]);
			}
			if(ans == 999999999){
				ans = -1;
			}
			Console.WriteLine(ans);
		}
	}
}