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
from heapq import heappush, heappop
import sys
input = sys.stdin.buffer.readline

N, Q = map(int, input().split())
E = []

for i in range(N):
    s, t, x = map(int, input().split())
    E.append((0, t - x, x, i))
    E.append((1, s - x, x, i))

D = [int(input()) for _ in range(Q)]

E.sort(key=lambda a: a[1], reverse=True)

ans = []
que = [(10**18, -1)]
V = set()
for d in D:
    while E and E[-1][1] <= d:
        f, _, x, i = E.pop()
        if f == 0:
            V.add(i)
        else:
            heappush(que, (x, i))
    while que[0][1] in V:
        heappop(que)
    ans.append(que[0][0])

ans = [a if a < 10**18 else -1 for a in ans]
print(*ans, sep='\n')
