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
# -*- coding: utf-8 -*-
import sys
from heapq import heappush, heappop
from bisect import bisect_left, bisect_right

N,Q=map(int, sys.stdin.readline().split())

S=[]
event=[]	#x, s, t
for _ in range(N):
	s,t,x=map(int, sys.stdin.readline().split())
	heappush( event, (x, max(0,s-x) , max(0,t-1-x)) )


D=[ int(sys.stdin.readline().strip()) for _ in range(Q) ]
D.sort()
ans=[ float("inf") for _ in range(Q) ]

Next=[ i+1 for i in range(Q) ]	#Next


while event:
	x,s,t=heappop(event)
	start=bisect_left(D,s)
	end=bisect_right(D,t)

	i=start
	while i<end:
		ans[i]=min(ans[i],x)
		next=Next[i]
		Next[i]=end
		i=next

for x in ans:
	if x==float("inf"):
		print -1
	else:
		print x

