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
#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
Created on Sat Jun 15 16:58:00 2019

@author: YudNK
"""
import bisect as bs

N, Q = map(int, input().split())
E = []
for i in range(N):
    s, t, x = map(int, input().split())
    a = [s - x, t - x, x] #イベント
    E.append(a)
E.sort(key = lambda x: x[2])
D = []
for i in range(Q):
    D.append(int(input()))

ans = [-1]*Q
check = [-1]*Q

for e in E:
    l = bs.bisect_left(D, e[0])
    r = bs.bisect_left(D, e[1])
    while l < r:
        if check[l] == -1:  
            ans[l] = e[2]
            check[l] = r
            l += 1
        else:
            l = check[l]
        
[print(i) for i in ans]