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
N, Q = [int(_) for _ in input().split()]
STX = [[int(_) for _ in input().split()] for _ in range(N)]
D = [int(input()) for _ in range(Q)]
events = []
for stx in STX:
    s, t, x = stx
    events += [[s - x, 1, x], [t - x, 0, x]]
for i in range(Q):
    events += [[D[i], 2, i]]
events.sort()
block = set()
ans = [-1] * Q
m = float('inf')
for e in events:
    if e[1] == 0:
        block.remove(e[2])
        if m == e[2]:
            if block:
                m = min(block)
            else:
                m = float('inf')
    elif e[1] == 1:
        block.add(e[2])
        m = min(m, e[2])
    else:
        if block:
            if m == float('inf'):
                ans[e[2]] = -1
            else:
                ans[e[2]] = m
print(*ans, sep='\n')
