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
# E - Roadwork
# https://atcoder.jp/contests/abc128/tasks/abc128_e

from heapq import heappop, heappush
from collections import defaultdict

n, q = map(int,input().split())
task = []
for _ in range(n): 
  s, t, x = map(int, input().split())
  task.append((t - x, 0, x)) 
  task.append((s - x, 1, x)) 

for i in range(q):
  d = int(input())
  task.append((d, 2, i)) 

answer = [-1] * q

task.sort()

se = set()
se_hp = []

for a, b, c in task:
  if b == 0:
    se.remove(c)
  elif b == 1:
    se.add(c)
    heappush(se_hp, c)
  else: # b == 2
    while se_hp and se_hp[0] not in se:
      heappop(se_hp)
    answer[c] = se_hp[0] if se_hp else -1

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