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 heappop,heappush

N,Q=map(int,input().split())


event=[]
q=[]
for _ in range(N):
    S,T,X=map(int,input().split())
    event.append([S-X,1,X])
    event.append([T-X,-1,X])

for i in range(Q):
    event.append([int(input()),2,i])

stop_set=set()
event.sort()
q=[]

for pos,m,x in event:
    if m==-1:
        stop_set.remove(x)
        
    elif m==1:
        #heappushする時点でqはソートされている
        heappush(q,x)
        stop_set.add(x)
    
    else:
        #この時点でのstop_setは、i番目の人が遭遇する通行止めの座標
        #この時点でのqは今までstopになった座標
        while q:
            #qはソート済なので、q[0]は最小値　それがstop_setから外れている場合、heappopでそれを排除する
            if q[0] not in stop_set:
                heappop(q)
            #q[0]がstop_setから外れてない場合、それ以降のqも外れていないのでbreak    
            else:
                break

        if q:
            print(q[0])
        else:
            print(-1)