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
#!/usr/bin/env python3
import sys, math, itertools, collections, bisect
input = lambda: sys.stdin.buffer.readline().rstrip().decode('utf-8')
# inf = float('inf') ;mod = 10**9+7
# mans = inf ;ans = 0 ;count = 0 ;pro = 1
from heapq import heappush,heappop

n,q=map(int,input().split())
STX=[tuple(map(int,input().split())) for i in range(n)]
D=[int(input()) for i in range(q)]
event=[]
for si,ti,xi in STX:
  event.append((si-xi,0,xi))
  event.append((ti-xi,-1,xi))
for di in D:
  event.append((di,1,di))
event.sort()
hq=[]; S=set()
for time, query, number in event:
  if query == 0:
    heappush(hq,number)
    S.add(number)
  elif query == -1:
    S.remove(number)
  else:
    while hq and hq[0] not in S:
      heappop(hq)
    if not hq:
      print(-1)
    else:
      print(hq[0])


