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 sys
input = sys.stdin.buffer.readline
from operator import itemgetter as get
from heapq import *


def main():
	n, q = map(int, input().split())
	event = []
	Xs = []
	for _ in range(n):
		s, t, x = map(int, input().split())
		event.append((-2, s - x, x))
		event.append((-1, t - x, x))
		Xs.append(x)
	for _ in range(q):
		d = int(input())
		event.append((0, d, None))
	event.sort(key=get(1))
	active = {x: 0 for x in Xs}
	candidate = []
	ans = []
	for flg, time, x in event:
		if flg == -2:
			active[x] = 1
			heappush(candidate, x)
		elif flg == -1:
			active[x] = 0
		else:
			res = -1
			while candidate:
				c = heappop(candidate)
				if active[c]:
					heappush(candidate, c)
					res = c
					break
			ans.append(res)
	print("\n".join(map(str, ans)))


if __name__ == '__main__':
	main()
