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: Accepted)

using System;
using System.Collections;
using System.Collections.Generic;
using System.Diagnostics;
using System.Globalization;
using System.IO;
using System.Text;
using System.Linq;

using E = System.Linq.Enumerable;
using System.Threading;

internal partial class Solver {
    public void Run() {
        var h = ni();
        var w = ni();
        var a = new int[h];
        var b = new int[h];
        for (int i = 0; i < h; i++) {
            a[i] = ni() - 1;
            b[i] = ni() - 1;
        }

        var seg = new MonoidOperator().CreateLazySegmentTree();
        seg.Build(w, i => new Monoid { Index = i, Value = i });
        var inf = new Monoid { Index = 0, Value = -100000000000L };
        for (int i = 0; i < h; i++) {
            if (a[i] == 0) {
                seg.LazyUpdate(0, b[i] + 1, -100000000000L);
            } else {
                seg.LazyUpdate(a[i], b[i] + 1, seg[a[i] - 1].Value);
            }
            var min = seg.Query(0, w).Exact;
            if (min > w) cout.WriteLine(-1);
            else cout.WriteLine(i + min + 1);
        }
    }
    static public bool withBug = false;
}

public struct Monoid {
    public long Index;
    public long Value;
    public long Exact => Index - Value;
    public object Dump() => new { Index, Value };
}


public class MonoidOperator : ILazySegmentTreeMonoidOperator<Monoid, long?> {
    public Monoid Identity => new Monoid { Index = 100000000000L, Value = -100000000000L };

    public long? OperatorIdentity => null;

    public Monoid Apply(Monoid monoid, int begin, int end, long? operation) {
        if (operation.HasValue) {
            monoid.Index = begin;
            monoid.Value = operation.Value;
        }
        return monoid;
    }

    public Monoid Merge(Monoid left, Monoid right) {
        if (left.Exact > right.Exact) return right;
        return left;
    }

    public long? MergeOperator(long? current, long? append) {
        return append ?? current;
    }
}

public interface ILazySegmentTreeMonoidOperator<TMonoid, TOperatorMonoid> {
    TMonoid Merge(TMonoid left, TMonoid right);
    TMonoid Apply(TMonoid monoid, int begin, int end, TOperatorMonoid operation);
    TOperatorMonoid MergeOperator(TOperatorMonoid current, TOperatorMonoid append);

    TMonoid Identity { get; }
    TOperatorMonoid OperatorIdentity { get; }
}

public static class LazySegmentTreeExtension {
    public static LazySegmentTree<TMonoid, TOperatorMonoid> CreateLazySegmentTree<TMonoid, TOperatorMonoid>
        (this ILazySegmentTreeMonoidOperator<TMonoid, TOperatorMonoid> lazySegmentTreeMonoidOperator) {
        return new LazySegmentTree<TMonoid, TOperatorMonoid>(
            lazySegmentTreeMonoidOperator.Merge,
            lazySegmentTreeMonoidOperator.Apply,
            lazySegmentTreeMonoidOperator.MergeOperator,
            lazySegmentTreeMonoidOperator.Identity,
            lazySegmentTreeMonoidOperator.OperatorIdentity
        );
    }

    public static bool Check<TMonoid, TOperatorMonoid>
        (this ILazySegmentTreeMonoidOperator<TMonoid, TOperatorMonoid> lazySegmentTreeMonoidOperator, TMonoid m, TOperatorMonoid o1, TOperatorMonoid o2) {
        var r1 = lazySegmentTreeMonoidOperator.Apply(lazySegmentTreeMonoidOperator.Apply(m, 1, 2, o1), 1, 2, o2);
        var r2 = lazySegmentTreeMonoidOperator.Apply(m, 1, 2, lazySegmentTreeMonoidOperator.MergeOperator(o1, o2));
        return r1.Equals(r2);
    }
}

public sealed class LazySegmentTree<TMonoid, TOperatorMonoid> {
    private int Count;
    private TMonoid[] _node;
    private TOperatorMonoid[] _operators;
    private int[] _height;
    private int[] _begin, _end;
    private readonly TMonoid _identity;
    private readonly TOperatorMonoid _operatorIdentity;
    private readonly Func<TMonoid, TMonoid, TMonoid> _merge;
    private readonly Func<TMonoid, int, int, TOperatorMonoid, TMonoid> _apply;
    private readonly Func<TOperatorMonoid, TOperatorMonoid, TOperatorMonoid> _mergeOperator;

    public LazySegmentTree(
        Func<TMonoid, TMonoid, TMonoid> merge,
        Func<TMonoid, int, int, TOperatorMonoid, TMonoid> apply,
        Func<TOperatorMonoid, TOperatorMonoid, TOperatorMonoid> mergeOperator,
        TMonoid identity,
        TOperatorMonoid operatorIdentity) {
        _merge = merge;
        _apply = apply;
        _mergeOperator = mergeOperator;
        _identity = identity;
        _operatorIdentity = operatorIdentity;
    }

    public void Build(IList<TMonoid> array) {
        Build(array.Count, i => array[i]);
    }

    public void Build(int n, Func<int, TMonoid> create) {
        Count = n;

        _node = new TMonoid[2 * Count];
        _operators = new TOperatorMonoid[2 * Count];
        _begin = new int[2 * Count];
        _end = new int[2 * Count];
        _height = new int[2 * Count];
        for (var i = 0; i < _node.Length; i++) {
            _node[i] = _identity;
            _operators[i] = _operatorIdentity;
        }

        for (var i = 0; i < n; i++) {
            _node[i + Count] = create(i);
            _begin[i + Count] = i;
            _end[i + Count] = i + 1;
        }

        for (var i = 2; i < _height.Length; i++) {
            _height[i] = _height[i >> 1] + 1;
        }

        for (var i = Count - 1; i > 0; i--) {
            _node[i] = _merge(_node[i << 1], _node[i << 1 | 1]);
            _begin[i] = _begin[i << 1];
            _end[i] = _end[i << 1 | 1];
        }
    }

    private void Propagate(int k) {
        int childL = k << 1, childR = childL | 1;
        _operators[childL] = _mergeOperator(_operators[childL], _operators[k]);
        _operators[childR] = _mergeOperator(_operators[childR], _operators[k]);
        _node[k] = Apply(k);
        _operators[k] = _operatorIdentity;
    }

    public TMonoid Query(int begin, int end) {
        TMonoid lv = _identity, rv = _identity;
        begin += Count;
        end += Count;
        TopDownOperators(begin);
        TopDownOperators(end - 1);
        for (int l = begin, r = end - 1; l <= r; l >>= 1, r >>= 1) {
            if ((l & 1) == 1) { lv = _merge(lv, Apply(l++)); }
            if ((r & 1) == 0) { rv = _merge(Apply(r--), rv); }
        }
        return _merge(lv, rv);
    }

    public void LazyUpdate(int begin, int end, TOperatorMonoid @operator) {
        begin += Count;
        end += Count;
        TopDownOperators(begin);
        TopDownOperators(end - 1);
        for (int l = begin, r = end - 1; l <= r; l >>= 1, r >>= 1) {
            if ((l & 1) == 1) { _operators[l] = _mergeOperator(_operators[l], @operator); l++; }
            if ((r & 1) == 0) { _operators[r] = _mergeOperator(_operators[r], @operator); r--; }
        }
        BottomUpMonoids(begin);
        BottomUpMonoids(end - 1);
    }

    public void Diagonsis() {
        for (var i = 1; i < Count; i++) {
            Propagate(i);
            var ex = _merge(Apply(i << 1), Apply(i << 1 | 1));
            var ex2 = Apply(i);
            if (!ex2.Equals(ex)) throw new Exception();
        }
    }

    private void TopDownOperators(int k) {
        for (var i = _height[k]; i > 0; i--) {
            Propagate(k >> i);
        }
    }

    private TMonoid Apply(int k) {
        return _apply(_node[k], _begin[k], _end[k], _operators[k]);
    }

    private void BottomUpMonoids(int k) {
        while ((k >>= 1) > 0) {
            _node[k] = _merge(Apply(k << 1), Apply(k << 1 | 1));
        }
    }

    public TMonoid this[int index] {
        get {
            index += Count;
            TopDownOperators(index);
            return Apply(index);
        }
        set {
            index += Count;
            TopDownOperators(index);
            _node[index] = value;
            _operators[index] = _operatorIdentity;
            BottomUpMonoids(index);
        }
    }
}


// PREWRITEN CODE BEGINS FROM HERE

static public class StringExtensions {
    static public string JoinToString<T>(this IEnumerable<T> source, string separator = " ") {
        return string.Join(separator, source);
    }
}

internal partial class Solver : Scanner {
    static readonly int? StackSizeInMebiByte = null; //50;
    public static void StartAndJoin(Action action, int maxStackSize) {
        var thread = new Thread(new ThreadStart(action), maxStackSize);
        thread.Start();
        thread.Join();
    }

    public static void Main() {
#if LOCAL
        byte[] inputBuffer = new byte[1000000];
        var inputStream = Console.OpenStandardInput(inputBuffer.Length);
        using (var reader = new StreamReader(inputStream, Console.InputEncoding, false, inputBuffer.Length)) {
            Console.SetIn(reader);
            new Solver(Console.In, Console.Out).Run();
        }
#else
        Console.SetOut(new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false });
        if (StackSizeInMebiByte.HasValue) {
            StartAndJoin(() => new Solver(Console.In, Console.Out).Run(), StackSizeInMebiByte.Value * 1024 * 1024);
        } else {
            new Solver(Console.In, Console.Out).Run();
        }
        Console.Out.Flush();
#endif
    }

#pragma warning disable IDE0052
    private readonly TextReader cin;
    private readonly TextWriter cout;
    private readonly TextWriter cerr;
#pragma warning restore IDE0052

    public Solver(TextReader reader, TextWriter writer)
        : base(reader) {
        cin = reader;
        cout = writer;
        cerr = Console.Error;
    }

    public Solver(string input, TextWriter writer)
        : this(new StringReader(input), writer) {
    }

#pragma warning disable IDE1006
#pragma warning disable IDE0051
    private int ni() { return NextInt(); }
    private int[] ni(int n) { return NextIntArray(n); }
    private long nl() { return NextLong(); }
    private long[] nl(int n) { return NextLongArray(n); }
    private double nd() { return NextDouble(); }
    private double[] nd(int n) { return NextDoubleArray(n); }
    private string ns() { return Next(); }
    private string[] ns(int n) { return NextArray(n); }
#pragma warning restore IDE1006
#pragma warning restore IDE0051
}

#if DEBUG
internal static class LinqPadExtension {
    public static string TextDump<T>(this T obj) {
        if (obj is IEnumerable) return (obj as IEnumerable).Cast<object>().JoinToString().Dump();
        else return obj.ToString().Dump();
    }
    public static T Dump<T>(this T obj) {
        return LINQPad.Extensions.Dump(obj);
    }
}
#endif

public class Scanner {
    private readonly TextReader Reader;
    private readonly CultureInfo ci = CultureInfo.InvariantCulture;

    private readonly char[] buffer = new char[2 * 1024];
    private int cursor = 0, length = 0;
    private string Token;
    private readonly StringBuilder sb = new StringBuilder(1024);

    public Scanner()
        : this(Console.In) {
    }

    public Scanner(TextReader reader) {
        Reader = reader;
    }

    public int NextInt() { return checked((int)NextLong()); }
    public long NextLong() {
        var s = Next();
        long r = 0;
        int i = 0;
        bool negative = false;
        if (s[i] == '-') {
            negative = true;
            i++;
        }
        for (; i < s.Length; i++) {
            r = r * 10 + (s[i] - '0');
#if DEBUG
            if (!char.IsDigit(s[i])) throw new FormatException();
#endif
        }
        return negative ? -r : r;
    }
    public double NextDouble() { return double.Parse(Next(), ci); }
    public string[] NextArray(int size) {
        string[] array = new string[size];
        for (int i = 0; i < size; i++) {
            array[i] = Next();
        }

        return array;
    }
    public int[] NextIntArray(int size) {
        int[] array = new int[size];
        for (int i = 0; i < size; i++) {
            array[i] = NextInt();
        }

        return array;
    }

    public long[] NextLongArray(int size) {
        long[] array = new long[size];
        for (int i = 0; i < size; i++) {
            array[i] = NextLong();
        }

        return array;
    }

    public double[] NextDoubleArray(int size) {
        double[] array = new double[size];
        for (int i = 0; i < size; i++) {
            array[i] = NextDouble();
        }

        return array;
    }

    public string Next() {
        if (Token == null) {
            if (!StockToken()) {
                throw new Exception();
            }
        }
        var token = Token;
        Token = null;
        return token;
    }

    public bool HasNext() {
        if (Token != null) {
            return true;
        }

        return StockToken();
    }

    private bool StockToken() {
        while (true) {
            sb.Clear();
            while (true) {
                if (cursor >= length) {
                    cursor = 0;
                    if ((length = Reader.Read(buffer, 0, buffer.Length)) <= 0) {
                        break;
                    }
                }
                var c = buffer[cursor++];
                if (33 <= c && c <= 126) {
                    sb.Append(c);
                } else {
                    if (sb.Length > 0) break;
                }
            }

            if (sb.Length > 0) {
                Token = sb.ToString();
                return true;
            }

            return false;
        }
    }
}