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, bisect_right
from operator import itemgetter
import sys
input = sys.stdin.readline


def main():
    N, Q = map(int, input().split())
    constructions = [None] * N
    for i in range(N):
        S, T, X = map(int, input().split())
        constructions[i] = (S, T, X)
    constructions.sort(key=itemgetter(2))
    D = [int(input()) for _ in range(Q)]
    ans = [-1] * Q
    nxt = list(range(1, Q+1))
    for S, T, X in constructions:
        l = bisect_left(D, S-X)
        r = bisect_right(D, T-X-1)
        idx = l
        while idx < r:
            if ans[idx] == -1:
                ans[idx] = X
            nidx = nxt[idx]
            nxt[idx] = max(nxt[idx], r)
            idx = nidx
    for a in ans:
        print(a)


if __name__ == "__main__":
    main()
