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 heapq

class BalancingTree:
    def __init__(self):
        self.p = []
        self.q = []

    def insert(self, x):
        heapq.heappush(self.p, x)

    def erase(self, x):
        heapq.heappush(self.q, x)

    def minimum(self):
        while self.q and self.p[0] == self.q[0]:
            heapq.heappop(self.p)
            heapq.heappop(self.q)
        return self.p[0] if self.p else -1


n, q = map(int, input().split())
events = []
for _ in range(n):
    s, t, x = map(int, input().split())
    events.append((s-x, 1, x))
    events.append((t-x, 0, x))
for _ in range(q):
    d = int(input())
    events.append((d, 2, 0))

events.sort()
bt = BalancingTree()
for _, i, k in events:
    if i == 1:
        bt.insert(k)
    elif i == 0:
        bt.erase(k)
    else:
        print(bt.minimum())
