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
import heapq
from collections import defaultdict
input = sys.stdin.buffer.readline
sys.setrecursionlimit(10 ** 7)

N, Q = map(int, input().split())
task = []
for _ in range(N):
    s, t, x = map(int, input().split())
    start = t - x
    end = s - x
    task.append((start, -1, x))
    task.append((end, 1, x))
task.sort(reverse=True)

cand = []
discard = defaultdict(int)
ans = []

for _ in range(Q):
    d = int(input())
    while task and task[-1][0] <= d:
        _, flag, x = task.pop()
        if flag == 1:
            heapq.heappush(cand, x)
        else:
            discard[x] += 1

    while cand:
        x = cand[0]
        if discard[x] > 0:
            heapq.heappop(cand)
            discard[x] -= 1
        else:
            break

    if cand:
        ans.append(cand[0])
    else:
        ans.append(-1)

print(*ans, sep="\n")