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 heappush, heappop
import sys

readline = sys.stdin.readline
N, Q = map(int, readline().split())
ans = [None]*Q
def solve(readline=readline):
    qs = [0]*(N+1)
    for i in range(N):
        s, t, x = map(int, readline().split())
        qs[i] = (s-x, t-x, x)
    qs[N] = (10**10, 10**10, 0)
    qs.sort()

    que = []
    D = [int(readline()) for i in range(Q)]
    j = 0
    it = iter(qs).__next__
    s, t, x = it()
    v = w = N
    for d in D:
        while j < N and s <= d:
            heappush(que, (x, t))
            v, w = que[0]
            s, t, x = it()
        while que and w <= d:
            heappop(que)
            if que:
                v, w = que[0]
        if que:
            yield "%d\n" % v
        else:
            yield "-1\n"
ans[:] = solve()
sys.stdout.writelines(ans)