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.

Example

Input

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


Output

2
2
10
-1
13
-1
import java.util.*;

public class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int q = sc.nextInt();
        PriorityQueue<Event> queue = new PriorityQueue<>();
        for (int i = 0; i < n; i++) {
            queue.add(new Event(sc.nextInt(), sc.nextInt(), sc.nextInt()));
        }
        TreeMap<Integer, Integer> map = new TreeMap<>();
        for (int i = 0; i < q; i++) {
            map.put(sc.nextInt(), i);
        }
        int[] ans = new int[q];
        Arrays.fill(ans, -1);
        while (queue.size() > 0) {
            Event e = queue.poll();
            Map.Entry<Integer, Integer> x = map.ceilingEntry(e.start - e.point);
            while (x != null && x.getKey() < e.end - e.point) {
                ans[x.getValue()] = e.point;
                map.remove(x.getKey());
                x = map.ceilingEntry(e.start - e.point);
            }
        }
        StringBuilder sb = new StringBuilder();
        for (int x : ans) {
            sb.append(x).append("\n");
        }
        System.out.print(sb);
    }
    
    static class Event implements Comparable<Event> {
        int start;
        int end;
        int point;
        
        public Event(int start, int end, int point) {
            this.start = start;
            this.end = end;
            this.point = point;
        }
        
        public int compareTo(Event another) {
            return point - another.point;
        }
    }
}