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.Generic;
using System.IO;
using System.Linq;
using static System.Math;
using System.Text;
using System.Threading;
using System.Globalization;
using System.Runtime.CompilerServices;
using Library;

namespace Program
{
    public static class ProblemF
    {
        static bool SAIKI = false;
        static public int numberOfRandomCases = 0;
        static public void MakeTestCase(List<string> _input, List<string> _output, ref Func<string[], bool> _outputChecker)
        {
        }
        static public void Solve()
        {
            var H = NN;
            var W = NN;
            var ABList = Repeat(0, H).Select(_ => new { A = NN - 1, B = NN }).ToArray();
            var seg = LIB_RedBlackTree.CreateRangeUpdateRangeMax();
            var kai = LIB_RedBlackTree.CreateRangeUpdateRangeMin();
            for (var i = 0; i < W; i++)
            {
                seg.Add(i, i);
                kai.Add(i, 0);
            }
            var left = 0L;
            var cnt = 0L;
            foreach (var item in ABList)
            {
                ++cnt;
                if (item.A <= left)
                {
                    left = Max(left, item.B);
                }
                var maxPos = seg.Query(item.A, item.B);
                if (item.B < W)
                {
                    var tmp = seg[item.B].Value;
                    maxPos = Max(maxPos, tmp);
                }
                var beforePos = -1L;
                if (left < item.A) beforePos = seg[item.A - 1].Value;
                seg.Update(item.A, item.B, beforePos);
                if (item.B < W)
                {
                    seg.Remove(item.B);
                    seg.Add(item.B, maxPos);
                }
                kai.Update(item.A, item.B, long.MaxValue);
                if (item.B < W)
                {
                    kai.Remove(item.B);
                    kai.Add(item.B, item.B - maxPos);
                }
                var ans = kai.Query(left, W);
                if (ans == long.MaxValue) Console.WriteLine(-1);
                else Console.WriteLine(ans + cnt);
            }
        }
        class Printer : StreamWriter
        {
            public override IFormatProvider FormatProvider { get { return CultureInfo.InvariantCulture; } }
            public Printer(Stream stream) : base(stream, new UTF8Encoding(false, true)) { base.AutoFlush = false; }
            public Printer(Stream stream, Encoding encoding) : base(stream, encoding) { base.AutoFlush = false; }
        }
        static LIB_FastIO fastio = new LIB_FastIODebug();
        static public void Main(string[] args) { if (args.Length == 0) { fastio = new LIB_FastIO(); Console.SetOut(new Printer(Console.OpenStandardOutput())); } if (SAIKI) { var t = new Thread(Solve, 134217728); t.Start(); t.Join(); } else Solve(); Console.Out.Flush(); }
        static long NN => fastio.Long();
        static double ND => fastio.Double();
        static string NS => fastio.Scan();
        static long[] NNList(long N) => Repeat(0, N).Select(_ => NN).ToArray();
        static double[] NDList(long N) => Repeat(0, N).Select(_ => ND).ToArray();
        static string[] NSList(long N) => Repeat(0, N).Select(_ => NS).ToArray();
        static long Count<T>(this IEnumerable<T> x, Func<T, bool> pred) => Enumerable.Count(x, pred);
        static IEnumerable<T> Repeat<T>(T v, long n) => Enumerable.Repeat<T>(v, (int)n);
        static IEnumerable<int> Range(long s, long c) => Enumerable.Range((int)s, (int)c);
        static IOrderedEnumerable<T> OrderByRand<T>(this IEnumerable<T> x) => Enumerable.OrderBy(x, _ => xorshift);
        static IOrderedEnumerable<T> OrderBy<T>(this IEnumerable<T> x) => Enumerable.OrderBy(x.OrderByRand(), e => e);
        static IOrderedEnumerable<T1> OrderBy<T1, T2>(this IEnumerable<T1> x, Func<T1, T2> selector) => Enumerable.OrderBy(x.OrderByRand(), selector);
        static IOrderedEnumerable<T> OrderByDescending<T>(this IEnumerable<T> x) => Enumerable.OrderByDescending(x.OrderByRand(), e => e);
        static IOrderedEnumerable<T1> OrderByDescending<T1, T2>(this IEnumerable<T1> x, Func<T1, T2> selector) => Enumerable.OrderByDescending(x.OrderByRand(), selector);
        static IOrderedEnumerable<string> OrderBy(this IEnumerable<string> x) => x.OrderByRand().OrderBy(e => e, StringComparer.OrdinalIgnoreCase);
        static IOrderedEnumerable<T> OrderBy<T>(this IEnumerable<T> x, Func<T, string> selector) => x.OrderByRand().OrderBy(selector, StringComparer.OrdinalIgnoreCase);
        static IOrderedEnumerable<string> OrderByDescending(this IEnumerable<string> x) => x.OrderByRand().OrderByDescending(e => e, StringComparer.OrdinalIgnoreCase);
        static IOrderedEnumerable<T> OrderByDescending<T>(this IEnumerable<T> x, Func<T, string> selector) => x.OrderByRand().OrderByDescending(selector, StringComparer.OrdinalIgnoreCase);
        static string Join<T>(this IEnumerable<T> x, string separator = "") => string.Join(separator, x);
        static uint xorshift { get { _xsi.MoveNext(); return _xsi.Current; } }
        static IEnumerator<uint> _xsi = _xsc();
        static IEnumerator<uint> _xsc() { uint x = 123456789, y = 362436069, z = 521288629, w = (uint)(DateTime.Now.Ticks & 0xffffffff); while (true) { var t = x ^ (x << 11); x = y; y = z; z = w; w = (w ^ (w >> 19)) ^ (t ^ (t >> 8)); yield return w; } }
    }
}
namespace Library {
    class LIB_RedBlackTree
    {
        public struct SumEntity
        {
            public long s;
            public long c;
        }
        static public LIB_RedBlackTree<long, long, long> CreateRangeUpdateRangeMin() => new LIB_RedBlackTree<long, long, long>(long.MaxValue, long.MinValue + 100, Math.Min, (x, y) => y, (x, y) => y);
        static public LIB_RedBlackTree<long, long, long> CreateRangeAddRangeMin() => new LIB_RedBlackTree<long, long, long>(long.MaxValue, 0, Math.Min, (x, y) => x + y, (x, y) => x + y);
        static public LIB_RedBlackTree<long, long, long> CreateRangeUpdateRangeMax() => new LIB_RedBlackTree<long, long, long>(long.MinValue, long.MaxValue - 100, Math.Max, (x, y) => y, (x, y) => y);
        static public LIB_RedBlackTree<long, long, long> CreateRangeAddRangeMax() => new LIB_RedBlackTree<long, long, long>(long.MinValue, 0, Math.Max, (x, y) => x + y, (x, y) => x + y);
        static public LIB_RedBlackTree<long, SumEntity, long> CreateRangeUpdateRangeSum() => new LIB_RedBlackTree<long, SumEntity, long>(new SumEntity { c = 0, s = 0 }, long.MaxValue, (x, y) => new SumEntity { c = x.c + y.c, s = x.s + y.s }, (x, y) => new SumEntity { c = x.c, s = x.c * y }, (x, y) => y);
        static public LIB_RedBlackTree<long, SumEntity, long> CreateRangeAddRangeSum() => new LIB_RedBlackTree<long, SumEntity, long>(new SumEntity { c = 0, s = 0 }, 0, (x, y) => new SumEntity { c = x.c + y.c, s = x.s + y.s }, (x, y) => new SumEntity { c = x.c, s = x.s + x.c * y }, (x, y) => x + y);
    }
    class LIB_RedBlackTree<Key, ValueT, ValueE> where ValueE : IEquatable<ValueE>
    {
        bool ope;
        class Node
        {
            public Node left;
            public Node right;
            public Key key;
            public ValueT val;
            public ValueT dat;
            public ValueE lazy;
            public bool isBlack;
            public int cnt;
            public bool needRecalc;
        }
        Func<ValueT, ValueT, ValueT> f;
        Func<ValueT, ValueE, ValueT> g;
        Func<ValueE, ValueE, ValueE> h;
        ValueT ti;
        ValueE ei;
        Comparison<Key> c;
        Node root;
        bool isNeedFix;
        Node lmax;
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public LIB_RedBlackTree(ValueT ti, ValueE ei, Func<ValueT, ValueT, ValueT> f, Func<ValueT, ValueE, ValueT> g, Func<ValueE, ValueE, ValueE> h, Comparison<Key> c, bool ope = true)
        {
            this.ti = ti;
            this.ei = ei;
            this.f = f;
            this.g = g;
            this.h = h;
            this.c = c;
            this.ope = ope;
        }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public LIB_RedBlackTree(ValueT ti, ValueE ei, Func<ValueT, ValueT, ValueT> f, Func<ValueT, ValueE, ValueT> g, Func<ValueE, ValueE, ValueE> h) : this(ti, ei, f, g, h, Comparer<Key>.Default.Compare) { }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        bool IsRed(Node n) => n != null && !n.isBlack;
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        bool IsBlack(Node n) => n != null && n.isBlack;
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        int Cnt(Node n) => n == null ? 0 : n.cnt;
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        void Eval(Node n)
        {
            if (n == null || ei.Equals(n.lazy)) return;
            n.val = g(n.val, n.lazy);
            if (!n.needRecalc) n.dat = g(n.dat, n.lazy);
            if (n.left != null) n.left.lazy = h(n.left.lazy, n.lazy);
            if (n.right != null) n.right.lazy = h(n.right.lazy, n.lazy);
            n.lazy = ei;
        }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        void Recalc(Node n)
        {
            if (n == null) return;
            Eval(n);
            if (!n.needRecalc) return;
            n.needRecalc = false;
            n.dat = n.val;
            if (n.left != null)
            {
                Recalc(n.left);
                n.dat = f(n.left.dat, n.dat);
            }
            if (n.right != null)
            {
                Recalc(n.right);
                n.dat = f(n.dat, n.right.dat);
            }
        }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        Node RotateL(Node n)
        {
            if (ope) { Eval(n); Eval(n.right); }
            Node m = n.right, t = m.left;
            m.left = n; n.right = t;
            n.cnt -= m.cnt - Cnt(t);
            m.cnt += n.cnt - Cnt(t);
            n.needRecalc = true; m.needRecalc = true;
            return m;
        }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        Node RotateR(Node n)
        {
            if (ope) { Eval(n); Eval(n.left); }
            Node m = n.left, t = m.right;
            m.right = n; n.left = t;
            n.cnt -= m.cnt - Cnt(t);
            m.cnt += n.cnt - Cnt(t);
            n.needRecalc = true; m.needRecalc = true;
            return m;
        }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        Node RotateLR(Node n)
        {
            n.left = RotateL(n.left);
            return RotateR(n);
        }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        Node RotateRL(Node n)
        {
            n.right = RotateR(n.right);
            return RotateL(n);
        }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public void Add(Key key, ValueT val)
        {
            root = Add(root, key, val);
            root.isBlack = true;
        }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        Node Add(Node n, Key key, ValueT val)
        {
            if (n == null)
            {
                isNeedFix = true;
                return new Node() { key = key, val = val, dat = val, lazy = ei, cnt = 1 };
            }
            if (ope) Eval(n);
            if (c(key, n.key) < 0) n.left = Add(n.left, key, val);
            else n.right = Add(n.right, key, val);
            n.needRecalc = true;
            ++n.cnt;
            return Balance(n);
        }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        Node Balance(Node n)
        {
            if (!isNeedFix || !IsBlack(n)) return n;
            if (IsRed(n.left) && IsRed(n.left.left))
            {
                n = RotateR(n);
                n.left.isBlack = true;
            }
            else if (IsRed(n.left) && IsRed(n.left.right))
            {
                n = RotateLR(n);
                n.left.isBlack = true;
            }
            else if (IsRed(n.right) && IsRed(n.right.left))
            {
                n = RotateRL(n);
                n.right.isBlack = true;
            }
            else if (IsRed(n.right) && IsRed(n.right.right))
            {
                n = RotateL(n);
                n.right.isBlack = true;
            }
            else isNeedFix = false;
            return n;
        }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public void Remove(Key key)
        {
            root = Remove(root, key);
            if (root != null) root.isBlack = true;
        }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        Node Remove(Node n, Key key)
        {
            if (ope) Eval(n);
            --n.cnt;
            var r = c(key, n.key);
            if (r < 0)
            {
                n.left = Remove(n.left, key);
                n.needRecalc = true;
                return BalanceL(n);
            }
            if (r > 0)
            {
                n.right = Remove(n.right, key);
                n.needRecalc = true;
                return BalanceR(n);
            }
            if (n.left == null)
            {
                isNeedFix = n.isBlack;
                return n.right;
            }
            n.left = RemoveMax(n.left);
            n.key = lmax.key;
            n.val = lmax.val;
            n.needRecalc = true;
            return BalanceL(n);
        }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        Node RemoveMax(Node n)
        {
            if (ope) Eval(n);
            --n.cnt;
            if (n.right != null)
            {
                n.right = RemoveMax(n.right);
                n.needRecalc = true;
                return BalanceR(n);
            }
            lmax = n;
            isNeedFix = n.isBlack;
            return n.left;
        }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        Node BalanceL(Node n)
        {
            if (!isNeedFix) return n;
            if (IsBlack(n.right) && IsRed(n.right.left))
            {
                var b = n.isBlack;
                n = RotateRL(n);
                n.isBlack = b;
                n.left.isBlack = true;
                isNeedFix = false;
            }
            else if (IsBlack(n.right) && IsRed(n.right.right))
            {
                var b = n.isBlack;
                n = RotateL(n);
                n.isBlack = b;
                n.right.isBlack = true;
                n.left.isBlack = true;
                isNeedFix = false;
            }
            else if (IsBlack(n.right))
            {
                isNeedFix = n.isBlack;
                n.isBlack = true;
                n.right.isBlack = false;
            }
            else
            {
                n = RotateL(n);
                n.isBlack = true;
                n.left.isBlack = false;
                n.left = BalanceL(n.left);
                isNeedFix = false;
            }
            return n;
        }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        Node BalanceR(Node n)
        {
            if (!isNeedFix) return n;
            if (IsBlack(n.left) && IsRed(n.left.right))
            {
                var b = n.isBlack;
                n = RotateLR(n);
                n.isBlack = b; n.right.isBlack = true;
                isNeedFix = false;
            }
            else if (IsBlack(n.left) && IsRed(n.left.left))
            {
                var b = n.isBlack;
                n = RotateR(n);
                n.isBlack = b;
                n.left.isBlack = true;
                n.right.isBlack = true;
                isNeedFix = false;
            }
            else if (IsBlack(n.left))
            {
                isNeedFix = n.isBlack;
                n.isBlack = true;
                n.left.isBlack = false;
            }
            else
            {
                n = RotateR(n);
                n.isBlack = true;
                n.right.isBlack = false;
                n.right = BalanceR(n.right);
                isNeedFix = false;
            }
            return n;
        }
        public KeyValuePair<Key, ValueT> this[long i]
        {
            [MethodImpl(MethodImplOptions.AggressiveInlining)]
            get { return At(root, i); }
        }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        KeyValuePair<Key, ValueT> At(Node n, long i)
        {
            if (ope) Eval(n);
            if (n.left == null)
            {
                if (i == 0) return new KeyValuePair<Key, ValueT>(n.key, n.val);
                else return At(n.right, i - 1);
            }
            if (n.left.cnt == i) return new KeyValuePair<Key, ValueT>(n.key, n.val);
            if (n.left.cnt > i) return At(n.left, i);
            return At(n.right, i - n.left.cnt - 1);
        }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public bool ContainsKey(Key key)
        {
            var t = LowerBound(key);
            return t < Cnt(root) && c(At(root, t).Key, key) == 0;
        }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public long UpperBound(Key key) => UpperBound(root, key);
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        long UpperBound(Node n, Key key)
        {
            if (n == null) return 0;
            var r = c(key, n.key);
            if (r < 0) return UpperBound(n.left, key);
            return Cnt(n.left) + 1 + UpperBound(n.right, key);
        }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public long LowerBound(Key key) => LowerBound(root, key);
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        long LowerBound(Node n, Key key)
        {
            if (n == null) return 0;
            var r = c(key, n.key);
            if (r <= 0) return LowerBound(n.left, key);
            return Cnt(n.left) + 1 + LowerBound(n.right, key);
        }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public KeyValuePair<Key, ValueT> Min()
        {
            Node n = root.left, p = root;
            while (n != null)
            {
                p = n;
                if (ope) Eval(p);
                n = n.left;
            }
            return new KeyValuePair<Key, ValueT>(p.key, p.val);
        }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public KeyValuePair<Key, ValueT> Max()
        {
            Node n = root.right, p = root;
            while (n != null)
            {
                p = n;
                if (ope) Eval(p);
                n = n.right;
            }
            return new KeyValuePair<Key, ValueT>(p.key, p.val);
        }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public void Update(long l, long r, ValueE val) => Update(root, l, r, val);
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        void Update(Node n, long l, long r, ValueE val)
        {
            if (n == null) return;
            Eval(n);
            n.needRecalc = true;
            var lc = Cnt(n.left);
            if (lc < l) Update(n.right, l - lc - 1, r - lc - 1, val);
            else if (r <= lc) Update(n.left, l, r, val);
            else if (l <= 0 && Cnt(n) <= r) n.lazy = val;
            else
            {
                n.val = g(n.val, val);
                if (l < lc) Update(n.left, l, lc, val);
                if (lc + 1 < r) Update(n.right, 0, r - lc - 1, val);
            }
            return;
        }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public ValueT Query(long l, long r) => Query(root, l, r);
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        ValueT Query(Node n, long l, long r)
        {
            var v1 = ti; var v2 = ti; var v3 = ti;
            if (n == null) return ti;
            Eval(n);
            var lc = Cnt(n.left);
            if (lc < l) v3 = Query(n.right, l - lc - 1, r - lc - 1);
            else if (r <= lc) v1 = Query(n.left, l, r);
            else if (l <= 0 && Cnt(n) <= r)
            {
                Recalc(n);
                v2 = n.dat;
            }
            else
            {
                if (l < lc) v1 = Query(n.left, l, lc);
                if (lc + 1 < r) v3 = Query(n.right, 0, r - lc - 1);
                v2 = n.val;
            }
            return f(f(v1, v2), v3);
        }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public bool Any() => root != null;
        public long Count => Cnt(root);
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public IEnumerable<KeyValuePair<Key, ValueT>> List() => L(root);
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        IEnumerable<KeyValuePair<Key, ValueT>> L(Node n)
        {
            if (n == null) yield break;
            foreach (var i in L(n.left)) yield return i;
            yield return new KeyValuePair<Key, ValueT>(n.key, n.val);
            foreach (var i in L(n.right)) yield return i;
        }
    }
    class LIB_RedBlackTree<Key, Value>
    {
        LIB_RedBlackTree<Key, Value, int> tree;
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public LIB_RedBlackTree(Comparison<Key> c) { tree = new LIB_RedBlackTree<Key, Value, int>(default(Value), 0, (x, y) => x, (x, y) => x, (x, y) => x, c, false); }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public LIB_RedBlackTree() : this(Comparer<Key>.Default.Compare) { }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public void Add(Key key, Value val) => tree.Add(key, val);
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public void Remove(Key key) => tree.Remove(key);
        public KeyValuePair<Key, Value> this[long i]
        {
            [MethodImpl(MethodImplOptions.AggressiveInlining)]
            get { return tree[i]; }
        }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public bool ContainsKey(Key key) => tree.ContainsKey(key);
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public long UpperBound(Key key) => tree.UpperBound(key);
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public long LowerBound(Key key) => tree.LowerBound(key);
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public KeyValuePair<Key, Value> Min() => tree.Min();
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public KeyValuePair<Key, Value> Max() => tree.Max();
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public bool Any() => tree.Any();
        public long Count => tree.Count;
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public IEnumerable<KeyValuePair<Key, Value>> List() => tree.List();
    }
    class LIB_RedBlackTree<T>
    {
        LIB_RedBlackTree<T, int, int> tree;
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public LIB_RedBlackTree(Comparison<T> c) { tree = new LIB_RedBlackTree<T, int, int>(0, 0, (x, y) => x, (x, y) => x, (x, y) => x, c, false); }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public LIB_RedBlackTree() : this(Comparer<T>.Default.Compare) { }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public void Add(T val) => tree.Add(val, 0);
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public void Remove(T val) => tree.Remove(val);
        public T this[long i]
        {
            [MethodImpl(MethodImplOptions.AggressiveInlining)]
            get { return tree[i].Key; }
        }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public bool ContainsKey(T val) => tree.ContainsKey(val);
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public long UpperBound(T val) => tree.UpperBound(val);
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public long LowerBound(T val) => tree.LowerBound(val);
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public T Min() => tree.Min().Key;
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public T Max() => tree.Max().Key;
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public bool Any() => tree.Any();
        public long Count => tree.Count;
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public IEnumerable<T> List() => tree.List().Select(e => e.Key);
    }
    class LIB_FastIO
    {
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public LIB_FastIO() { str = Console.OpenStandardInput(); }
        readonly Stream str;
        readonly byte[] buf = new byte[1024];
        int len, ptr;
        public bool isEof = false;
        public bool IsEndOfStream
        {
            [MethodImpl(MethodImplOptions.AggressiveInlining)]
            get { return isEof; }
        }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        byte read()
        {
            if (isEof) throw new EndOfStreamException();
            if (ptr >= len)
            {
                ptr = 0;
                if ((len = str.Read(buf, 0, 1024)) <= 0)
                {
                    isEof = true;
                    return 0;
                }
            }
            return buf[ptr++];
        }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        char Char()
        {
            byte b = 0;
            do b = read();
            while (b < 33 || 126 < b);
            return (char)b;
        }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        virtual public string Scan()
        {
            var sb = new StringBuilder();
            for (var b = Char(); b >= 33 && b <= 126; b = (char)read())
                sb.Append(b);
            return sb.ToString();
        }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        virtual public long Long()
        {
            long ret = 0; byte b = 0; var ng = false;
            do b = read();
            while (b != '-' && (b < '0' || '9' < b));
            if (b == '-') { ng = true; b = read(); }
            for (; true; b = read())
            {
                if (b < '0' || '9' < b)
                    return ng ? -ret : ret;
                else ret = ret * 10 + b - '0';
            }
        }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        virtual public double Double() { return double.Parse(Scan(), CultureInfo.InvariantCulture); }
    }
    class LIB_FastIODebug : LIB_FastIO
    {
        Queue<string> param = new Queue<string>();
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        string NextString() { if (param.Count == 0) foreach (var item in Console.ReadLine().Split(' ')) param.Enqueue(item); return param.Dequeue(); }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public LIB_FastIODebug() { }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public override string Scan() => NextString();
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public override long Long() => long.Parse(NextString());
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public override double Double() => double.Parse(NextString());
    }
}