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
#D in [S_i-X_i,T_i-X_i) → Xiで止まる
import sys
input = sys.stdin.readline
from heapq import heappop,heappush
from collections import defaultdict

N,Q = map(int,input().split())
task = []

STX = [[int(x) for x in input().split()] for _ in range(N)]
for s,t,x in STX:
  task.append((t-x,0,x)) # xで止まらなくなる
  task.append((s-x,1,x)) # xで止まる

for i in range(Q):
  d = int(input())
  task.append((d,2,i)) # 止まる位置を答える
answer = [-1]*Q

task.sort()

# 引っかかってる場所の管理
se = set()
se_hp = [] # heapでソートを保つ

# 小さい時刻から順に見ていく
for a,b,c in task:
  if not b: # b == 0
    se.remove(c)
  elif b&1: # 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)))
