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 bisect
import sys
input = sys.stdin.readline
'''
allinputs = iter(input().splitlines())
input = lambda : next(allinputs)
#'''

N, Q = map(int, input().split())
S, T, X = [0] * N, [0] * N, [0] * N
work = []

for i in range(N):
	S[i], T[i], X[i] = map(int, input().split())
	work.append((X[i], S[i] - X[i], T[i] - X[i]))

D = [int(input()) for _ in range(Q)]

work.sort()
ans = [-1] * Q
skip = [-1] * Q

for i in range(N):
	left = bisect.bisect_left(D, work[i][1])
	right = bisect.bisect_left(D, work[i][2])
	
	while left < right:
		if skip[left] == -1:
			skip[left] = right
			ans[left] = work[i][0]
			left += 1
		else:
			left = skip[left]					
		
for i in ans:
	print(i)
	