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
from bisect import bisect_left


def main():
    N, Q, *I = map(int, open(0).read().split())
    STX, D = I[:3 * N], I[3 * N:]

    E = sorted(zip(*[iter(STX)] * 3), key=lambda x: x[2])

    R = [-1] * Q
    ans = [-1] * Q

    for s, t, x in E:
        l = bisect_left(D, s - x)
        r = bisect_left(D, t - x)
        while l < r:
            if R[l] == -1:
                ans[l] = x
                R[l] = r
                l += 1
            else:
                l = R[l]

    print(*ans, sep='\n')


if __name__ == '__main__':
    main()
