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
N, Q = map(int, input().split())
# The person start in this location will be stopped.
work = []
for i in range(N):
    start, end, pos = map(int, input().split())
    work.append((start - pos - 0.5, end - pos - 0.5, pos))
work.sort(key=lambda x: x[0])
depart_time = [int(input()) for _ in range(Q)]
heap = []
end_time = {}
import heapq
i = 0
for depart in depart_time:
    while i < len(work) and work[i][0] < depart:
        start, end, pos = work[i]
        heapq.heappush(heap, pos)
        end_time[pos] = end
        i += 1
    while heap and end_time[heap[0]] < depart:
        heapq.heappop(heap)
    if heap: print(heap[0])
    else: print(-1)


