Problem:
Score : 500 points

Problem Statement

There is an infinitely long street that runs west to east, which we consider as a number line.

There are N roadworks scheduled on this street.
The i-th roadwork blocks the point at coordinate X_i from time S_i - 0.5 to time T_i - 0.5.

Q people are standing at coordinate 0. The i-th person will start the coordinate 0 at time D_i, continue to walk with speed 1 in the positive direction and stop walking when reaching a blocked point.

Find the distance each of the Q people will walk.

Constraints

All values in input are integers.

1 \leq N, Q \leq 2 \times 10^5

0 \leq S_i < T_i \leq 10^9

1 \leq X_i \leq 10^9

0 \leq D_1 < D_2 < ... < D_Q \leq 10^9

If i \neq j and X_i = X_j, the intervals [S_i, T_i) and [S_j, T_j) do not overlap.

Input

Input is given from Standard Input in the following format:

N Q
S_1 T_1 X_1
:
S_N T_N X_N
D_1
:
D_Q

Output

Print Q lines. The i-th line should contain the distance the i-th person will walk or -1 if that person walks forever.

Sample Input 1

4 6
1 3 2
7 13 10
18 20 13
3 4 2
0
1
2
3
5
8

Sample Output 1

2
2
10
-1
13
-1

The first person starts coordinate 0 at time 0 and stops walking at coordinate 2 when reaching a point blocked by the first roadwork at time 2.

The second person starts coordinate 0 at time 1 and reaches coordinate 2 at time 3. The first roadwork has ended, but the fourth roadwork has begun, so this person also stops walking at coordinate 2.

The fourth and sixth persons encounter no roadworks while walking, so they walk forever. The output for these cases is -1.

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 N = NN;
            var Q = NN;
            var stx = Repeat(0, N).Select(_ => new { s = NN, t = NN, x = NN }).ToArray();
            var dList = NNList(Q);

            var douro = new List<Tuple<long, long, long>>((int)(N * 2 + Q));
            foreach (var item in stx)
            {
                douro.Add(Tuple.Create(item.s - item.x, 1L, item.x));
                douro.Add(Tuple.Create(item.t - item.x, -1L, item.x));
            }
            foreach (var item in dList)
            {
                douro.Add(Tuple.Create(item, 2L, 0L));
            }
            var kouji = new LIB_RedBlackTree<long>();
            foreach (var item in douro.OrderByRand().OrderBy(e => e.Item1).ThenBy(e => e.Item2))
            {
                if (item.Item2 == 1)
                {
                    kouji.Add(item.Item3);
                }
                if (item.Item2 == 2)
                {
                    if (kouji.Any())
                    {
                        Console.WriteLine(kouji.Min());
                    }
                    else
                    {
                        Console.WriteLine(-1);
                    }
                }
                if (item.Item2 == -1)
                {
                    kouji.Remove(item.Item3);
                }
            }
        }
        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_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());
    }
    class LIB_RedBlackTree
    {
        public struct SumEntity
        {
            public long s;
            public long c;
        }
        static public LIB_RedBlackTree<long, long, long> CreateRUQRmQ() => new LIB_RedBlackTree<long, long, long>(long.MaxValue, long.MaxValue, Math.Min, (x, y) => y, (x, y) => y);
        static public LIB_RedBlackTree<long, long, long> CreateRAQRmQ() => 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> CreateRUQRMQ() => new LIB_RedBlackTree<long, long, long>(long.MinValue, long.MinValue, Math.Max, (x, y) => y, (x, y) => y);
        static public LIB_RedBlackTree<long, long, long> CreateRAQRMQ() => 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> CreateRUQRSQ() => 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> CreateRAQRSQ() => 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);
    }
}