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 heapify,heappop,heappush
import sys
read=sys.stdin.readline
class mset:
    def __init__(self):
        self.p,self.q=[],[]
        heapify(self.p);heapify(self.q)
    def add(self,a):
        heappush(self.p,a)
    def delete(self,a):
            heappush(self.q,a)
    def minimum(self):
        while self.q and self.p[0]==self.q[0]:
            heappop(self.p);heappop(self.q)
        return self.p[0] if self.p else None

N,Q=map(int,read().split())
event=[]
for i in range(N):
    S,T,X=map(int,read().split())
    event.append((1,S-X,X))
    event.append((0,T-X,X))

s=mset()
now=0
for i in range(Q):
    D=int(read())
    event.append((2,D,0))
event.sort(key=lambda x:(x[1],x[0]))

for c,t,w in event:
    if c==0:
        s.delete(w)
    elif c==1:
        s.add(w)
    else:
        m=s.minimum()
        print(-1 if m==None else m)