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
from bisect import bisect_left
n, Q = list(map(int, input().split()))
stx = [list(map(int, input().split())) for i in range(n)]
q = [int(input()) for i in range(Q)]
stx.sort(key=lambda x: x[2])
ans = [-1 for i in range(Q)]
skip = [-1 for i in range(Q)]

for (s, t, x) in stx:
  begin = bisect_left(q, s-x)
  end = bisect_left(q, t-x)
  while begin<end:
    if skip[begin]==-1:
      ans[begin] = x
      skip[begin] = end
      begin += 1
    else:
      begin = skip[begin]
for e in ans:
  print(e)