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
import sys
input = sys.stdin.readline

from heapq import heappop, heappush
from collections import defaultdict

N, Q = map(int, input().split())

lst = []
for i in range(N):
    s, t, x = map(int, input().split())
    lst.append((t - x, 0, x)) #xで止まらなくなる
    lst.append((s - x, 1, x)) #xで止まる

for i in range(Q):
    lst.append((int(input()), 2, i))

lst.sort()
ans = [-1] * Q

#引っかかっている場所の管理
se = set()
se_hp = [] #heapで最小値を先頭に保つ

#小さい時刻から順に見ていく
for a, b, c in lst:
    if b == 0:
        se.remove(c)
    elif b == 1:
        se.add(c)
        heappush(se_hp, c)
    else:
        while se_hp and se_hp[0] not in se:
            heappop(se_hp)
        ans[c] = se_hp[0] if se_hp else -1

print ('\n'.join(map(str, ans)))