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)

use std::cmp::Ordering;

#[derive(Eq, PartialEq, 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)
    }
}
fn is_left(position: i64, s: i64, x: i64) -> bool {
    if position + s <= x {
        true
    } else {
        false
    }
}
fn is_right(position: i64, t: i64, x: i64) -> bool {
    if position + t > x {
        true
    } else {
        false
    }
}
const INF: i32 = 1000000000;
fn solve() {
    let s = std::io::stdin();
    let mut sc = Scanner { stdin: s.lock() };
    let n: usize = sc.read();
    let q: usize = sc.read();
    let mut obstacles: Vec<(i64, i64, i64)> = (0..n)
        .map(|_| {
            let s: i64 = sc.read();
            let t: i64 = sc.read();
            let x: i64 = sc.read();
            (s, t, x)
        })
        .collect();
    obstacles.sort_by(|a, b| a.2.cmp(&b.2));

    let walkers: Vec<i64> = (0..q)
        .map(|_| {
            let d: i64 = sc.read();
            -d
        })
        .collect();
    let mut answers = vec![INF; q];
    let mut left_values = vec![vec![]; q];
    let mut right_values = vec![vec![]; q];
    for &obstacle in obstacles.iter() {
        let s = obstacle.0;
        let t = obstacle.1;
        let x = obstacle.2;
        let mut left_value = None;
        let mut right_value = None;
        //left
        {
            let mut left = -1;
            let mut right = (q + 1) as i32;
            while right - left > 1 {
                let med = (right + left) / 2;
                if med < 0 {
                    left = med;
                    continue;
                }
                if med >= q as i32 {
                    right = med;
                    continue;
                }
                let med = med as usize;
                if is_left(walkers[med], s, x) {
                    right = med as i32;
                    right_value = Some(med);
                } else {
                    left = med as i32;
                }
            }
        }
        //right
        {
            let mut left = -1;
            let mut right = (q + 1) as i32;
            while right - left > 1 {
                let med = (right + left) / 2;
                if med < 0 {
                    left = med;
                    continue;
                }
                if med >= q as i32 {
                    right = med;
                    continue;
                }
                let med = med as usize;

                if is_right(walkers[med], t, x) {
                    left = med as i32;
                    left_value = Some(med);
                } else {
                    right = med as i32;
                }
            }
        }

        if left_value.is_none() || right_value.is_none() {
            continue;
        }

        let left_value = left_value.unwrap();
        let right_value = right_value.unwrap();
        left_values[left_value].push(x);
        right_values[right_value].push(x);
    }
    let mut heap: std::collections::BinaryHeap<Rev<i64>> = vec![].into_iter().map(Rev).collect();
    let mut degrees: std::collections::HashMap<i64, i32> = std::collections::HashMap::new();
    for i in 0..q {
        while let Some(value) = right_values[i].pop() {
            heap.push(Rev(value));
            *degrees.entry(value).or_insert(0) += 1;
        }
        while let Some(&Rev(value)) = heap.peek() {
            if *degrees.get(&value).unwrap() > 0 {
                break;
            } else {
                heap.pop();
            }
        }
        if let Some(&Rev(val)) = heap.peek() {
            assert!(*degrees.get(&val).unwrap() > 0);
            answers[i] = std::cmp::min(answers[i], val as i32);
        }

        while let Some(value) = left_values[i].pop() {
            *degrees.entry(value).or_insert(0) -= 1;
        }

        //pop
        while let Some(&Rev(value)) = heap.peek() {
            if *degrees.get(&value).unwrap() > 0 {
                break;
            } else {
                heap.pop();
            }
        }
        // println!("");
    }

    for ans in answers {
        let ans = if ans == INF { -1 } else { ans };
        println!("{}", ans);
    }
}

fn main() {
    std::thread::Builder::new()
        .stack_size(64 * 1024 * 1024) // 64MB
        .spawn(|| solve())
        .unwrap()
        .join()
        .unwrap();
}

//snippet from kenkoooo
pub struct Scanner<R> {
    stdin: R,
}

impl<R: std::io::Read> Scanner<R> {
    pub fn read<T: std::str::FromStr>(&mut self) -> T {
        use std::io::Read;
        let buf = self
            .stdin
            .by_ref()
            .bytes()
            .map(|b| b.unwrap())
            .skip_while(|&b| b == b' ' || b == b'\n' || b == b'\r')
            .take_while(|&b| b != b' ' && b != b'\n' && b != b'\r')
            .collect::<Vec<_>>();
        unsafe { std::str::from_utf8_unchecked(&buf) }
            .parse()
            .ok()
            .expect("Parse error.")
    }
    pub fn read_line(&mut self) -> String {
        use std::io::Read;
        let buf = self
            .stdin
            .by_ref()
            .bytes()
            .map(|b| b.unwrap())
            .skip_while(|&b| b == b'\n' || b == b'\r')
            .take_while(|&b| b != b'\n' && b != b'\r')
            .collect::<Vec<_>>();
        unsafe { std::str::from_utf8_unchecked(&buf) }
            .parse()
            .ok()
            .expect("Parse error.")
    }
    pub fn vec<T: std::str::FromStr>(&mut self, n: usize) -> Vec<T> {
        (0..n).map(|_| self.read()).collect()
    }

    pub fn chars(&mut self) -> Vec<char> {
        self.read::<String>().chars().collect()
    }
}