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
from heapq import heappop, heappush

input = sys.stdin.readline
N, Q = map(int, input().split())
event_list = []
for i in range(N):
  s, t, x = map(int, input().split())
  event_list.append([s-x, 1, x])
  event_list.append([t-x, -1, x])

for i in range(Q):
  event_list.append([int(input()), 2, 0])

ans = []
event_list.sort()
x_set = set()
x_list = []
for time, event, x in event_list:
  if event == 1:
    x_set.add(x)
    heappush(x_list, x)
  elif event == -1:
    x_set.remove(x)
  else:
    while x_list and x_list[0] not in x_set:
      heappop(x_list)
    if x_list:
      ans.append(x_list[0])
    else:
      ans.append(-1)

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