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
import sys
input=sys.stdin.readline
N,Q=map(int,input().split())

event_list=[]
for i in range(N):
  S,T,X=map(int,input().split())
  event_list.append((S-X-0.5,1,X))
  event_list.append((T-X-0.5,-1,X))
  
dlist=[]
for i in range(Q):
  D=int(input())
  event_list.append((D,0,X))  
  dlist.append(D)
event_list.sort()
#print(event_list)

answer_dic={}
stop_set=set()
min_set=float("inf")
for t,f,x in event_list:
  if f==1:
    stop_set.add(x)
    if x<min_set:
      min_set=x
  elif f==-1:
    stop_set.remove(x)
    if x==min_set:
      if len(stop_set)>0:
        min_set=min(stop_set)
      else:
        min_set=float("inf")
  else:
    if len(stop_set)>0:
      answer_dic[t]=min_set
    else:
      answer_dic[t]=-1
#print(answer_dic)

for d in dlist:
  print(answer_dic[d])