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
read = sys.stdin.read
import heapq

n, q = map(int, input().split())
STX = [list(map(int, input().split())) for _ in range(n)]
D = list(map(int, read().split()))
E = []
for s, t, x in STX:
  E.append((s-x, x, 1))
  E.append((t-x, x, 0))
E.sort(reverse=True)
que = []
stop = set()
que.append(10**10)
stop.add(10**10)
for d in D:
  while E and E[-1][0] <= d:
    temp, x, f = E.pop()
    if f:
      heapq.heappush(que, x)
      stop.add(x)
    else:
      stop.remove(x)
  while que[0] not in stop:
    heapq.heappop(que)
  if que[0] == 10**10:
    print(-1)
  else:
    print(que[0])