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# (.NET Core 3.1.201) (judge verdict: Runtime Error)

using System.Linq;
using System.Text;
using System;
using System.Collections;
using System.Collections.Generic;
using System.Globalization;
using System.IO;
using System.Diagnostics;
using System.Threading;
using System.Runtime.CompilerServices;
using System.IO.Pipes;

namespace AtCoder
{
    class Program
    {

        struct Point
        {
            public int x;
            public int y;

            public Point(int x, int y)
            {

                this.x = x;
                this.y = y;

            }

        }


        const int BiggestMod = 1000000007;

        public static void Main()
        {

            var args = Console.ReadLine().Split(' ').Select(x => int.Parse(x)).ToArray();

            var h = args[0];
            var w = args[1];

            var ans = new int[h];

            for (int i = 0; i < h; i++)
                ans[i] = -1;

            for (int i = w; 0 < i; i--)
            {

                int now = i;

                for (int j = 0; j < h; j++)
                {

                    args = Console.ReadLine().Split(' ').Select(x => int.Parse(x)).ToArray();

                    int buf = 0;

                    if (args[0] <= now && now <= args[1])
                    {

                        buf = args[1] + 1 - now;
                        now = args[1] + 1;

                    }

                    buf++;

                    if (w < now) break;
                    else ans[j] = (j != 0 ? ans[j - 1] : 0) + buf;

                }
            }
            foreach (var an in ans)
                Console.WriteLine(an);


        }

    }

}