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
import heapq
n, q = map(int, input().split())
stx = [tuple(map(int, input().split())) for _ in range(n)]
d = [int(input()) for _ in range(q)]

events = []
for s, t, x in stx:
    events.append((s-x, 1, x))
    events.append((t-x, -1, x))
events.sort(key=lambda x: x[0])

hp = []
st = set()
res = [-1] * q
now = 0
for t, b, x in events:
    while now < q and d[now] < t:
        if len(st) > 0:
            while hp[0] not in st:
                heapq.heappop(hp)
            res[now] = hp[0]
        now += 1
    if b == 1:
        heapq.heappush(hp, x)
        st.add(x)
    else:
        st.discard(x)
print(*res)