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 bisect
import heapq
import sys
N,Q = [int(x) for x in sys.stdin.readline().split()]

hitos = []
ans = [-1 for _ in range(Q)]
queries =[]
jump = ans[::]



queries = [[int(x) for x in sys.stdin.readline().split()] for i in range(N)]
hitos = [int(sys.stdin.readline()) for i in range(Q)]


# for i in range(N):
    # S,T,X =list(map(int,input().split(" ")))
    # lt = S -X -0.5
    # rt = T -X -0.5
    # queries.append([lt,rt,X]) #-1 → 挿入クエリ lが時間、-1がクエリの種類、Xが場所


queries.sort(key=lambda x:x[2])





for l,r,x in queries:
     lind  = bisect.bisect_left(hitos,l-x - 0.5)
     rind  = bisect.bisect_left(hitos,r -x - 0.5)
     while lind < rind:
         if ans[lind] == -1:
            ans[lind] = x
            jump[lind] = rind
            lind += 1
         else:

             lind = jump[lind]

for i  in ans:
    print(i)
