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
import sys
sys.setrecursionlimit(10 ** 7)
read = sys.stdin.buffer.read
readline = sys.stdin.buffer.readline
readlines = sys.stdin.buffer.readlines


n,q=map(int,readline().split())

stx=[[int(x) for x in readline().split()] for _ in range(n)]
event=[]
for s,t,x in stx:
    event.append((s-x,1,x))
    event.append((t-x,-1,x))

for i in range(q):
    event.append((int(readline()),2,i))
event.sort()

ans=[0]*q

stop=set()
hq=[]
for t,op,x in event:
    if op==1:
        heappush(hq,x)
        stop.add(x)
    elif op==-1:
        stop.remove(x)

    else:
        while hq and hq[0] not in stop:
            heappop(hq) 
        ans[x]=hq[0] if hq else -1
    
for x in ans:
    print(x)