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]);
		long[,]A = new long[H,2];
		for(var i=0;i<H;i++){
			string[] str2 = Console.ReadLine().Split();
			A[i,0] = long.Parse(str2[0])-1;
			A[i,1] = long.Parse(str2[1])-1;
		}
		var list = new HashSet<long>();
		list.Add((long)(W-1) * 1000000);
		for(var i=0;i<H;i++){
			long k = 999999999;
			var list2 = new HashSet<long>();
			var list3 = new HashSet<long>();
			foreach(var L in list){
				long L1 = L / 1000000000000;
				long L2 = L / 1000000 % 1000000;
				if(L2 < A[i,0] || L1 > A[i,1]){
				} else if(L1 < A[i,0]){
					long L3 = L % 1000000;
					list3.Add(L);
					list2.Add(L1 * 1000000000000 + (A[i,0]-1) * 1000000 + L3);
					if(A[i,1] < W-1){
						if(L2 <= A[i,1]){
							k = Math.Min(k,A[i,1]-L2+L3+1);
						} else {
							list2.Add((A[i,1]+1) * 1000000000000 + L2 * 1000000 + L3);
						}
					}
				} else if(L2 <= A[i,1]){
					long L3 = L % 1000000;
					list3.Add(L);
					if(A[i,1] < W-1){
						k = Math.Min(k,A[i,1]-L2+L3+1);
					}
				} else {
					long L3 = L % 1000000;
					list3.Add(L);
					if(A[i,1] < W-1){
						k = Math.Min(k,L3);
						list2.Add((A[i,1]+1) * 1000000000000 + L2 * 1000000 + Math.Min(k,L3));
					}
				}
			}
			foreach(var L in list3){
				list.Remove(L);
			}
			foreach(var L in list2){
				list.Add(L);
			}
			if(k < 999999999){
				list.Add((A[i,1]+1) * 1000000000000 + (A[i,1]+1) * 1000000 + k);
			}
			long ans = 999999999;
			foreach(var L in list){
				ans = Math.Min(ans,L % 1000000);
			}
			if(ans == 999999999){
				ans = -1;
			} else {
				ans = ans + i + 1;
			}
			Console.WriteLine(ans);
		}
	}
}