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 heapq
from collections import deque
N, Q = map( int, input().split())
H = [(0,0,0) for _ in range(N)]
for i in range(N):
    s, t, x = map( int, input().split())
    H[i] = (x-t+1, x-s, x)
D = [ ( -int( input()), i) for i in range(Q)]
D.sort()
H.sort()
d = deque(H)
q = []
ANS = [0]*Q
for i in range(Q):
    t, j = D[i]
    while d:
        if d[0][0] <= t:
            _, s, x = d.popleft()
            heapq.heappush(q,(x,s))
        else:
            break
    while q:
        if q[0][1] >= t:
            break
        heapq.heappop(q)
    if not q:
        ANS[j] = -1
    else:
        ANS[j] = q[0][0]
for ans in ANS:
    print( ans)
