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.io.PrintWriter;
import java.util.*;

public class Main {
    static Scanner scanner = new Scanner(System.in);

    public static void main(String[]$) {
        int n = Integer.parseInt(scanner.next());
        int q = Integer.parseInt(scanner.next());
        List<State> list = new ArrayList<>();
        for (int i = 0; i < n; i++) {
            int s = Integer.parseInt(scanner.next());
            int t = Integer.parseInt(scanner.next());
            int x = Integer.parseInt(scanner.next());
            list.add(new State(s - x, x, -1));
            list.add(new State(t - x, x, -2));
        }
        int[] ans = new int[q];
        for (int i = 0; i < q; i++) {
            list.add(new State(Integer.parseInt(scanner.next()), 0, i));
        }
        Collections.sort(list);
        TreeSet<Integer> set = new TreeSet<>();
        for (State s : list) {
            if (s.v == -1) {
                set.add(s.d);
            } else if (s.v == -2) {
                set.remove(s.d);
            } else {
                ans[s.v] = set.isEmpty() ? -1 : set.first();
            }
        }

        PrintWriter out = new PrintWriter(System.out);
        for (int i : ans) {
            out.println(i);
        }
        out.flush();
    }

    static class State implements Comparable<State> {
        int t, d, v;

        State(int t, int d, int v) {
            this.t = t;
            this.d = d;
            this.v = v;
        }

        @Override
        public int compareTo(State o) {
            return Integer.compare(t, o.t);
        }
    }
}