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 bisect import bisect_left as bisect
N,Q = map(int,input().split())
event = [tuple(map(int,input().split())) for i in range(N)]
D = [int(input()) for i in range(Q)]

event.sort(key=lambda x:x[2])

ans = [-1]*Q
neg = [-1]*Q

for s,t,x in event:
    l = bisect(D,s-x)
    r = bisect(D,t-x)
    t = l
    while t < r:
        if neg[t] == -1:
            ans[t] = x
            neg[t] = r
            t += 1
        else:
            t = neg[t]

for i in range(Q):
    print(ans[i])