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# (Mono 4.6.2.0) (judge verdict: Time Limit Exceeded)

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

public class Prog
{
    private const int INF = 1000000007;
    private struct Pair { public int x, y; public Pair(int x, int y) { this.x = x; this.y = y; } }
    public static void Main()
    {
        int N = NextInt();
        int Q = NextInt();
        // zip[圧縮後] = 元座標
        Dictionary<Tuple<int,int>, int> zip = new Dictionary<Tuple<int,int>, int>();
        List<int[]> stx = Enumerable.Range(0, N).Select(v => LineInt()).ToList().OrderBy(x => x[2]).ToList();
        List<int> D = Enumerable.Range(0, Q).Select(v => NextInt()).ToList();
        PriorityQueue<int, int> inPQ = new PriorityQueue<int, int>();
        PriorityQueue<int, int> outPQ = new PriorityQueue<int, int>();
        int key = 0;
        int num = -INF;
        for (int i = 0; i < N; i++)
        {
            if (num != stx[i][2]) { zip[Tuple.Create(key,key)] = stx[i][2]; key++; num = stx[i][2]; }
            inPQ.Add(stx[i][0] - stx[i][2], key);
            outPQ.Add(stx[i][1] - stx[i][2], key);
        }
        MinTree MT = new MinTree(key + 1, 0);
        foreach (var e in D)
        {
            while (inPQ.Count() != 0)
                if (e >= inPQ.PeekKey()) MT.Add(inPQ.Take(), 1);
                else break;
            while (outPQ.Count() != 0)
                if (e >= outPQ.PeekKey()) MT.Add(outPQ.Take(), -1);
                else break;
            int ind = MT.MLS(1);
            Console.WriteLine(ind == -1 ? -1 : zip[Tuple.Create(ind - 1, ind - 1)]);
        }
    }
}

public class MinTree
{
    private List<int> table = new List<int>();
    private static int size = 1;
    private static int high = 1;
    public MinTree(int n, int k = 0)
    {
        while (size < n) size *= 2;
        high = (int)Math.Log(size, 2);
        for (int i = 0; i < 2 * size - 1; i++) table.Add(k);
    }
    public void Add(int x, int v)
    {
        x += size - 1;
        table[x] += v;
        table[x] = Math.Max(0, table[x]);
        while (x != 0)
        {
            x = (x % 2 == 0 ? x / 2 - 1 : x / 2);
            table[x] = table[x * 2 + 1] + table[x * 2 + 2];
        }
    }
    public int MLS(int k)
    {
        if (table.First() == 0) return -1;
        int index = 0;
        for (int y = 0; y < high; y++)
        {
            int left = index * 2 + 1;
            int right = index * 2 + 2;
            if (table[left] >= k) index = left;
            else { k -= table[left]; index = right; }
        }
        return index - size + 1;
    }
    public int GetValue(int k) { return table[k + size - 1]; }
}

public class PriorityQueue<Tkey, Tvalue> where Tkey : IComparable
{
    private List<Tkey> keys = new List<Tkey>();
    private List<Tvalue> values = new List<Tvalue>();
    private int size = 0;
    private bool Descending;
    private int Compare(Tkey a, Tkey b) { return (Descending ? a.CompareTo(b) : b.CompareTo(a)); }

    public PriorityQueue(bool b = true) { Clear(); Descending = b; }
    public int Count() { return size; }
    public void Clear() { keys = new List<Tkey>(); values = new List<Tvalue>(); size = 0; }
    public void Add(Tkey e, Tvalue v)
    {
        keys.Add(e);
        values.Add(v);
        int x = size;
        size += 1;
        while (x != 0)
        {
            int par = (x % 2 == 0 ? x - 2 : x - 1) / 2;
            if (Compare(keys[par], e) <= 0) break;
            Tkey a = keys[x]; keys[x] = keys[par]; keys[par] = a;
            Tvalue b = values[x]; values[x] = values[par]; values[par] = b;
            x = par;
        }
    }
    public void Poll()
    {
        Tkey k = keys[size - 1];
        Tvalue v = values[size - 1];
        int x = 0;
        size--;
        if (size == 0) { Clear(); return; }
        keys.RemoveAt(size);
        values.RemoveAt(size);
        while (true)
        {
            int l = x * 2 + 1;
            int r = x * 2 + 2;
            if (size - 1 < l) break;
            int y = 0;
            if (size - 1 == l) { y = l; }
            else if (Compare(keys[l], keys[r]) == 1) { y = r; }
            else { y = l; }
            if (Compare(keys[y], k) > 0) break;
            keys[x] = keys[y];
            values[x] = values[y];
            x = y;
        }
        keys[x] = k;
        values[x] = v;
    }
    public Tvalue Take() { Tvalue ret = values[0]; Poll(); return ret; }
    public Tvalue Peek() { return values[0]; }
    public Tkey PeekKey() { return keys[0]; }
    public void Debug()
    {
        Console.Write("key   : ");
        foreach (var k in keys) Console.Write(k + " ");
        Console.WriteLine();
        Console.Write("value : ");
        foreach (var k in values) Console.Write(k + " ");
        Console.WriteLine();
    }
}

public class Input
{
    private static Queue<string> q = new Queue<string>();
    private static void Confirm() { if (q.Count == 0) foreach (var s in Console.ReadLine().Split(' ')) q.Enqueue(s); }
    public static int NextInt() { Confirm(); return int.Parse(q.Dequeue()); }
    public static long NextLong() { Confirm(); return long.Parse(q.Dequeue()); }
    public static char NextChar() { Confirm(); return char.Parse(q.Dequeue()); }
    public static string NextString() { Confirm(); return q.Dequeue(); }
    public static double NextDouble() { Confirm(); return double.Parse(q.Dequeue()); }
    public static int[] LineInt() { return Console.ReadLine().Split(' ').Select(int.Parse).ToArray(); }
    public static long[] LineLong() { return Console.ReadLine().Split(' ').Select(long.Parse).ToArray(); }
    public static string[] LineString() { return Console.ReadLine().Split(' ').ToArray(); }
    public static double[] LineDouble() { return Console.ReadLine().Split(' ').Select(double.Parse).ToArray(); }
}