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 heapq

def main():
    N, Q = map(int, input().split())
    STX = [tuple(map(int, input().split())) for _ in range(N)]
    ev = []
    for s, t, x in STX:
        ev.append((s - x, True, x))
        ev.append((t - x, False, x))
    ev.sort(reverse=True)
    bar = []
    dead = {}

    for d in [int(input()) for _ in range(Q)]:
        while ev and ev[-1][0] <= d:
            t, a, x = ev.pop()
            if a:
                heapq.heappush(bar, x)
            else:
                dead[x] = dead.get(x, 0) + 1
                while bar and bar[0] in dead:
                    x = heapq.heappop(bar)
                    if dead[x] == 1:
                        del dead[x]
                    else:
                        dead[x] = dead[x] - 1
        print(bar[0] if bar else -1)

main()
