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
import heapq
from operator import itemgetter
from bisect import bisect_right
N, Q = map(int, input().split())
Stop = []
for i in range(N):
    S, T, X = map(int, input().split())
    Stop.append([S - X, X, 0, i])
    Stop.append([T - X, X, 1, i])
Stop.sort(key=itemgetter(0))
q = []
notClosed = [False]*N
A = [(-1, -1)]
for time, pos, lr, idx in Stop:
    if lr==0:
        heapq.heappush(q, (pos, idx))
    else:
        notClosed[idx] = True
        while len(q)>0 and notClosed[q[0][1]]:
            aaa = heapq.heappop(q)[1]

    if len(q):
        A.append((time, q[0][0]))
    else:
        A.append((time, -1))
A0 = list(map(itemgetter(0), A))
for _ in range(Q):
    D = int(input())
    idx = bisect_right(A0, D)

    print(A[idx-1][1])
