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 Rust (1.15.1) (judge verdict: Accepted)

//! ----------------------------------------------
//! Framework <https://github.com/vain0x/procon>
//!
//! See the bottom of file for solution.
//! ----------------------------------------------

#![allow(unused_imports)]
#![allow(non_snake_case)]

use std::cell::RefCell;
use std::cmp::{max, min, Ordering};
use std::collections::*;
use std::fmt::{Debug, Display, Formatter, Write as FmtWrite};
use std::io::{stderr, stdin, BufRead, Write};
use std::mem::{replace, swap};
use std::ops::*;
use std::rc::Rc;

/// Print values to standard error if debug mode.
#[allow(unused_macros)]
macro_rules! debug {
    ($($e:expr),*) => {
        #[cfg(debug_assertions)]
        $({
            let (e, mut err) = (stringify!($e), stderr());
            writeln!(err, "\x1B[33m{}\x1B[0m = {:?}", e, $e).unwrap()
        })*
    };
}

/// Read from standard input and parse each word.
/// - `read!(T, U, ..)` parses a line as a tuple of words.
/// - `read![[T]]` parses a line as an array of words.
/// - `read![..; N]` parses `N` lines, using `read!(..)` repeatedly.
#[allow(unused_macros)]
macro_rules! read {
    ([$t:ty] ; $n:expr) =>
        ((0..$n).map(|_| read!([$t])).collect::<Vec<_>>());
    ($($t:ty),+ ; $n:expr) =>
        ((0..$n).map(|_| read!($($t),+)).collect::<Vec<_>>());
    ([$t:ty]) =>
        (rl().split_whitespace().map(|w| w.parse().unwrap()).collect::<Vec<$t>>());
    ($($t:ty),*) => {{
        let buf = rl();
        let mut w = buf.split_whitespace();
        ($(w.next().unwrap().parse::<$t>().unwrap()),*)
    }};
}

/// Read a line from standard input.
#[allow(dead_code)]
fn rl() -> String {
    let mut buf = String::new();
    stdin().read_line(&mut buf).unwrap();

    #[allow(deprecated)]
    buf.trim_right().to_owned()
}

// -----------------------------------------------
// Solution
// -----------------------------------------------

#[derive(PartialEq, Eq, Clone, Debug)]
pub struct Rev<T>(pub T);

impl<T: PartialOrd> PartialOrd for Rev<T> {
    fn partial_cmp(&self, other: &Rev<T>) -> Option<Ordering> {
        other.0.partial_cmp(&self.0)
    }
}

impl<T: Ord> Ord for Rev<T> {
    fn cmp(&self, other: &Rev<T>) -> Ordering {
        other.0.cmp(&self.0)
    }
}

#[derive(Clone, Copy, Debug)]
enum Event {
    /// 位置 x を通行止め集合に入れる
    Push(i64),
    /// 位置 x を通行止め集合から取り除く
    Pop(i64),
    /// 人 i の歩行距離を計算する
    Query(usize),
}

fn main() {
    let (N, Q) = read!(usize, usize);
    let T = read![i64, i64, i64; N];
    let D = read![i64; Q];

    let mut E = vec![];
    for (s, t, x) in T {
        // 時刻 s - x に位置 x が通行止めになる
        E.push((s - x, Event::Push(x)));
        // 時刻 t - x に位置 x が通行止めでなくなる
        E.push((t - x, Event::Pop(x)));
    }
    for i in 0..D.len() {
        // 時刻 D(i) に人 i が歩き出す
        E.push((D[i], Event::Query(i)));
    }

    // 時刻についてソート
    E.sort_by(|&(ref lt, _), &(ref rt, _)| lt.cmp(rt));

    // 通行止めの集合 (最小値を取りたいのでヒープ)
    let mut queue = BinaryHeap::new();

    // 通行止めの集合から除去された要素の多重集合
    let mut removal = BTreeMap::new();

    // W[i] = i番目の人の歩行距離
    let mut W = vec![0; Q];

    for (_, e) in E {
        match e {
            Event::Push(x) => {
                queue.push(Rev(x));
            }
            Event::Pop(x) => {
                // removal[x] の値を1増やす
                *removal.entry(x).or_insert(0) += 1;
            }
            Event::Query(i) => {
                let mut min_x = -1;

                // ヒープから最小値を取る
                // ただし除外要素がトップにあるときは除去する
                while let Some(&Rev(x)) = queue.peek() {
                    match removal.get(&x) {
                        Some(&n) if n > 0 => {
                            // x は除外要素
                            queue.pop();
                            *removal.get_mut(&x).unwrap() -= 1;
                            continue;
                        }
                        _ => {
                            min_x = x;
                            break;
                        }
                    }
                }

                W[i] = min_x;
            }
        }
    }

    for w in W {
        println!("{}", w);
    }
}