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
from heapq import heappush, heappop
N,Q,*L = map(int, open(0).read().split())
X = L[:3*N]
D = L[3*N:]
ls = []
for s,t,x in zip(*[iter(X)]*3):
  ls.append((s-x,1,x))
  ls.append((t-x,0,x))
for i,d in enumerate(D):
  ls.append((d,2,i))
ls.sort()
ans = [0]*Q
S = set()
hq = []
for a,b,c in ls:
  if b==0:
    S.remove(c)
  elif b==1:
    S.add(c)
    heappush(hq,c)
  else:
    while hq and hq[0] not in S:
      heappop(hq)
    ans[c] = hq[0] if hq else -1
print('\n'.join(map(str,ans)))