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 = list(map(int, input().split()))
  STX = tuple(list(map(int, input().split())) for _ in range(N))
  D = tuple([int(input()) for _ in range(Q)])

  L = []
  for s, t, x in STX:
    L.append((x, s - x, t - x))

  L.sort(key = lambda x: x[1])
  q = []
  cnt = 0
  push = heapq.heappush
  pop = heapq.heappop
  t = []
  for i in range(Q):
    while cnt < len(L) and D[i] >= L[cnt][1]:
      if t != []:
        push(q, t)
        t = []
      push(q, L[cnt])
      cnt += 1
    if t != [] and t[2] > D[i]:
      print(t[0])
    else:
      while q != []:
        t = pop(q)
        if t[2] > D[i]:
          print(t[0])
          break
      else:
        t = []
        print(-1)

main()
