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 static System.Math;
using System.Linq;
using System.Collections.Generic;
using System;

public class SB_BinarySearchTree<T> where T : IComparable
{
    public class Node
    {
        public T Value;
        public Node LChild;
        public Node RChild;
        public int Count;

        public Node(T v)
        {
            Value = v;
            Count = 1;
        }
    }

    static Random _rnd = new Random();

    public static int Count(Node t)
    {
        return t == null ? 0 : t.Count;
    }

    static Node Update(Node t)
    {
        t.Count = Count(t.LChild) + Count(t.RChild) + 1;
        return t;
    }

    public static Node Merge(Node l, Node r)
    {
        if (l == null || r == null) return l == null ? r : l;

        if (Count(l) / (double)(Count(l) + Count(r)) > _rnd.NextDouble())
        {
            l.RChild = Merge(l.RChild, r);
            return Update(l);
        }
        else
        {
            r.LChild = Merge(l, r.LChild);
            return Update(r);
        }
    }

    public static Tuple<Node, Node> Split(Node t, int k)
    {
        if (t == null) return new Tuple<Node, Node>(null, null);
        if (k <= Count(t.LChild))
        {
            var s = Split(t.LChild, k);
            t.LChild = s.Item2;
            return new Tuple<Node, Node>(s.Item1, Update(t));
        }
        else
        {
            var s = Split(t.RChild, k - Count(t.LChild) - 1);
            t.RChild = s.Item1;
            return new Tuple<Node, Node>(Update(t), s.Item2);
        }
    }

    public static Node Remove(Node t, T v)
    {
        if (Find(t, v) == null) return t;
        return RemoveAt(t, LowerBound(t, v));
    }

    public static Node RemoveAt(Node t, int k)
    {
        var s = Split(t, k);
        var s2 = Split(s.Item2, 1);
        return Merge(s.Item1, s2.Item2);
    }

    public static bool Contains(Node t, T v)
    {
        return Find(t, v) != null;
    }

    public static Node Find(Node t, T v)
    {
        while (t != null)
        {
            var cmp = t.Value.CompareTo(v);
            if (cmp > 0) t = t.LChild;
            else if (cmp < 0) t = t.RChild;
            else break;
        }
        return t;
    }

    public static Node FindByIndex(Node t, int idx)
    {
        if (t == null) return null;

        var currentIdx = Count(t) - Count(t.RChild) - 1;
        while (t != null)
        {
            if (currentIdx == idx) return t;
            if (currentIdx > idx)
            {
                t = t.LChild;
                currentIdx -= (Count(t == null ? null : t.RChild) + 1);
            }
            else
            {
                t = t.RChild;
                currentIdx += (Count(t == null ? null : t.LChild) + 1);
            }
        }

        return null;
    }

    public static int UpperBound(Node t, T v)
    {
        var torg = t;
        if (t == null) return -1;

        var ret = int.MaxValue;
        var idx = Count(t) - Count(t.RChild) - 1;
        while (t != null)
        {
            var cmp = t.Value.CompareTo(v);

            if (cmp > 0)
            {
                ret = Min(ret, idx);
                t = t.LChild;
                idx -= (Count(t == null ? null : t.RChild) + 1);
            }
            else if (cmp <= 0)
            {
                t = t.RChild;
                idx += (Count(t == null ? null : t.LChild) + 1);
            }
        }
        return ret == int.MaxValue ? Count(torg) : ret;
    }

    public static int LowerBound(Node t, T v)
    {
        var torg = t;
        if (t == null) return -1;

        var idx = Count(t) - Count(t.RChild) - 1;
        var ret = int.MaxValue;
        while (t != null)
        {
            var cmp = t.Value.CompareTo(v);
            if (cmp >= 0)
            {
                if (cmp == 0) ret = Min(ret, idx);
                t = t.LChild;
                if (t == null) ret = Min(ret, idx);
                idx -= t == null ? 0 : (Count(t.RChild) + 1);
            }
            else if (cmp < 0)
            {
                t = t.RChild;
                idx += (Count(t == null ? null : t.LChild) + 1);
                if (t == null) return idx;
            }
        }
        return ret == int.MaxValue ? Count(torg) : ret;
    }

    public static Node Insert(Node t, T v)
    {
        var ub = LowerBound(t, v);
        return InsertByIdx(t, ub, v);
    }

    static Node InsertByIdx(Node t, int k, T v)
    {
        var s = Split(t, k);
        return Merge(Merge(s.Item1, new Node(v)), s.Item2);
    }

    public static IEnumerable<T> Enumerate(Node t)
    {
        var ret = new List<T>();
        Enumerate(t, ret);
        return ret;
    }

    static void Enumerate(Node t, List<T> ret)
    {
        if (t == null) return;
        Enumerate(t.LChild, ret);
        ret.Add(t.Value);
        Enumerate(t.RChild, ret);
    }
}

public class Set<T> where T : IComparable
{
    protected SB_BinarySearchTree<T>.Node _root;

    public T this[int idx] { get { return ElementAt(idx); } }

    public int Count()
    {
        return SB_BinarySearchTree<T>.Count(_root);
    }

    public virtual void Insert(T v)
    {
        if (_root == null) _root = new SB_BinarySearchTree<T>.Node(v);
        else
        {
            if (SB_BinarySearchTree<T>.Find(_root, v) != null) return;
            _root = SB_BinarySearchTree<T>.Insert(_root, v);
        }
    }

    public void Clear()
    {
        _root = null;
    }

    public void Remove(T v)
    {
        _root = SB_BinarySearchTree<T>.Remove(_root, v);
    }

    public bool Contains(T v)
    {
        return SB_BinarySearchTree<T>.Contains(_root, v);
    }

    public T ElementAt(int k)
    {
        var node = SB_BinarySearchTree<T>.FindByIndex(_root, k);
        if (node == null) throw new IndexOutOfRangeException();
        return node.Value;
    }

    public int Count(T v)
    {
        return SB_BinarySearchTree<T>.UpperBound(_root, v) - SB_BinarySearchTree<T>.LowerBound(_root, v);
    }

    public int LowerBound(T v)
    {
        return SB_BinarySearchTree<T>.LowerBound(_root, v);
    }

    public int UpperBound(T v)
    {
        return SB_BinarySearchTree<T>.UpperBound(_root, v);
    }

    public Tuple<int, int> EqualRange(T v)
    {
        if (!Contains(v)) return new Tuple<int, int>(-1, -1);
        return new Tuple<int, int>(SB_BinarySearchTree<T>.LowerBound(_root, v), SB_BinarySearchTree<T>.UpperBound(_root, v) - 1);
    }

    public List<T> ToList()
    {
        return new List<T>(SB_BinarySearchTree<T>.Enumerate(_root));
    }
}

public class MultiSet<T> : Set<T> where T : IComparable
{
    public override void Insert(T v)
    {
        if (_root == null) _root = new SB_BinarySearchTree<T>.Node(v);
        else _root = SB_BinarySearchTree<T>.Insert(_root, v);
    }
}

public class P : IComparable
{
    public int w0 { get; set; }
    public int now { get; set; }
    public int CompareTo(object obj)
    {
        var x = (P)obj;
        if (this.now > x.now) return 1;
        else if (this.now == x.now) return 0;
        else return -1;
    }
}


public class Hello
{
    public static int h, w;
    public static void Main()
    {
        string[] line = Console.ReadLine().Trim().Split(' ');
        h = int.Parse(line[0]);
        w = int.Parse(line[1]);
        var s = new int[h];
        var e = new int[h];
        for (int i = 0; i < h; i++)
        {
            line = Console.ReadLine().Trim().Split(' ');
            s[i] = int.Parse(line[0]) - 1;
            e[i] = int.Parse(line[1]) - 1;
        }
        getAns(s, e);
    }
    static void getAns(int[] s, int[] e)
    {
        var ms = new Set<P>();
        var ms2 = new MultiSet<int>();
        for (int i = 0; i < w; i++)
        {
            ms.Insert(new P { w0 = i, now = i });
            ms2.Insert(0);
        }
        for (int i = 0; i < h; i++)
        {
            var a = ms.LowerBound(new P { now = s[i] });
            var remo = new List<P>();
            var rmax = -1;
            while (a < ms.Count())
            {
                var aw = ms.ElementAt(a);
                if (aw.now >= s[i] && aw.now <= e[i])
                {
                    remo.Add(new P { w0 = aw.w0, now = aw.now });
                    rmax = Max(rmax, aw.w0);
                }
                else break;
                a++;
            }
            if (remo.Count() > 0)
            {
                foreach (var x in remo)
                {
                    ms.Remove(x);
                    ms2.Remove(x.now - x.w0);
                }
                if (e[i] < w - 1)
                {
                    ms.Insert(new P { w0 = rmax, now = e[i] + 1 });
                    ms2.Insert(e[i] + 1 - rmax);
                }
            }
            if (ms2.Count() == 0) Console.WriteLine(-1);
            else Console.WriteLine(ms2.ElementAt(0) + i + 1);
        }
    }
}