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: Time Limit Exceeded)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;

public class AtCoderA
{
    static void Main()
    {
        var sc = new Scanner();

        int h = sc.NextInt();
        int w = sc.NextInt();

        int[] dpBefore = new int[w];
        for (int i = 0; i < w; i++)
        {
            dpBefore[i] = 0;
        }

        int[] dpAfter = new int[w];
        for (int i = 0; i < w; i++)
        {
            dpAfter[i] = int.MaxValue;
        }

        for (int i = 1; i <= h; i++)
        {
            bool[] blocks = new bool[w];
            int a = sc.NextInt() - 1;
            int b = sc.NextInt() - 1;
            for (int j = a; j <= b; j++)
            {
                blocks[j] = true;
            }
            int answer = int.MaxValue;
            for (int j = 0; j < w; j++)
            {
                if (!blocks[j] && dpBefore[j] != int.MaxValue)
                {
                    dpAfter[j] = Math.Min(dpAfter[j], dpBefore[j] + 1);
                }
                if (j != 0 && dpAfter[j - 1] != int.MaxValue)
                {
                    dpAfter[j] = Math.Min(dpAfter[j], dpAfter[j - 1] + 1);
                }
                answer = Math.Min(answer, dpAfter[j]);
            }
            if (answer != int.MaxValue)
            {
                Console.WriteLine(answer);
            }
            else
            {
                Console.WriteLine(-1);
            }
            for (int j = 0; j < w; j++)
            {
                dpBefore[j] = dpAfter[j];
            }
            for (int j = 0; j < w; j++)
            {
                dpAfter[j] = int.MaxValue;
            }
        }
    }

    class Scanner
    {
        private string[] _line;
        private int _index;
        private const char Separator = ' ';

        public Scanner()
        {
            _line = new string[0];
            _index = 0;
        }

        public string Next()
        {
            while (_index >= _line.Length)
            {
                _line = Console.ReadLine().Split(Separator);
                _index = 0;
            }

            return _line[_index++];
        }

        public int NextInt() => int.Parse(Next());
        public long NextLong() => long.Parse(Next());
        public double NextDouble() => double.Parse(Next());
        public decimal NextDecimal() => decimal.Parse(Next());
        public char NextChar() => Next()[0];
        public char[] NextCharArray() => Next().ToCharArray();

        public string[] Array()
        {
            _line = Console.ReadLine().Split(Separator);
            _index = _line.Length;
            return _line;
        }

        public int[] IntArray() => Array().Select(int.Parse).ToArray();
        public long[] LongArray() => Array().Select(long.Parse).ToArray();
        public double[] DoubleArray() => Array().Select(double.Parse).ToArray();
        public decimal[] DecimalArray() => Array().Select(decimal.Parse).ToArray();
    }
}