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 heapify, heappush, heappop
import sys
input = sys.stdin.readline

def solve():
    N, Q = map(int, input().split())
    events = []
    for i in range(N):
        S, T, X = map(int, input().split())
        events.append((S-X-0.5, 1, X))
        events.append((T-X-0.5, 0, X))
    for i in range(Q):
        D = int(input())
        events.append((D, 2, i))

    events.sort()

    anss = [-1] * Q
    PQ = []
    isClosed = dict()
    for tm, tp, x in events:
        if tp == 0:
            isClosed[x] = 0
        elif tp == 1:
            isClosed[x] = 1
            heappush(PQ, x)
        else:
            while PQ:
                if isClosed[PQ[0]] == 1:
                    anss[x] = PQ[0]
                    break
                heappop(PQ)

    print('\n'.join(map(str, anss)))


solve()
