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 bisect import bisect_left



N,Q = map(int, input().split())
lines = sys.stdin.readlines()
kkk = []
for line in lines[:N]:
  s, t, x = map(int, line.split())
  kkk.append((x, s, t))
kkk.sort()
ddd = list(map(int, lines[N:]))

ans = [-1] * Q
skip = [-1] * Q
for x, s, t in kkk:
  ss = bisect_left(ddd, s - x)
  tt = bisect_left(ddd, t - x)
  while ss < tt:
    sk = skip[ss]
    if sk == -1:
      ans[ss] = x
      skip[ss] = tt
      ss += 1
    else:
      ss = sk

print('\n'.join(map(str, ans)))
