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.readline
read = sys.stdin.read

import heapq

def main():
  n, q = map(int, input().split())
  event = []
  stop = set()
  minque = []
  for _ in range(n):
    s, t, x = map(int, input().split())
    event.append((s-x, 1, x))
    event.append((t-x, -1, x))
  event.sort()
  event.append((float("inf"), 0, 0))
  D = list(map(int, read().split()))
  now = 0
  for t, b, x in event:
    while minque and minque[0] not in stop:
      heapq.heappop(minque)
    m = minque[0] if minque else -1
    while t > D[now]:
      print(m)
      now += 1
      if now == q:
        exit()
    if b == 1:
      stop.add(x)
      heapq.heappush(minque, x)
    else:
      stop.remove(x)
      
if __name__ == "__main__":
  main()