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 re
import math
import fractions
import random
from heapq import heappop,heappush
import time
import sys
input = sys.stdin.readline
#import numpy as np

 

 
#main
N,Q=map(int,input().split())
E=[]
for a in range(N):
    s,t,x=map(int,input().split())
    E.append((s-x,1,x))
    E.append((t-x,0,x))

for a in range(Q):
    E.append((int(input()),2,0))
E.sort()
 
S=set()
H=[]
for time_,type_,x in E:
    if type_&1:
        S.add(x)
        heappush(H,x)
    elif not type_:
        S.remove(x)
    else:
        while H and H[0] not in S:
            heappop(H)
        print(H[0] if H else -1)