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

sr = lambda: sys.stdin.readline().rstrip()
ir = lambda: int(sr())
lr = lambda: list(map(int, sr().split()))

N, Q = lr()
STX = [tuple(lr()) for _ in range(N)]
event = []
for s, t, x in STX:
    event.append((s-x, 0, x))
    event.append((t-x, -1, x))

for i in range(Q):
    d = ir()
    event.append((d, 1, i))

event.sort()
answer = [-1] * Q
cur = set()
flag = False
INF = 10 ** 10
min_x = INF
for a, b, c in event:
    if b == 0:
        cur.add(c)
        if c < min_x:
            min_x = c
            flag = True
    elif b == -1:
        cur.remove(c)
        if min_x == c:
            flag = False
    elif b == 1:
        if cur:
            if not flag:
                min_x = min(cur)
                flag = True
            answer[c] = min_x

print('\n'.join(map(str, answer)))
# 19