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 collections
 
 
def main():
    range = xrange
    input = raw_input
    from sys import stdin, stdout
 
    def read():
        return stdin.readline().rstrip('\n')
 
    def read_array(sep=None, maxsplit=-1):
        return read().split(sep, maxsplit)
 
    def read_int():
        return int(read())
 
    def read_int_array(sep=None, maxsplit=-1):
        return [int(a) for a in read_array(sep, maxsplit)]
 
    def write(*args, **kwargs):
        sep = kwargs.get('sep', ' ')
        end = kwargs.get('end', '\n')
        stdout.write(sep.join(str(a) for a in args) + end)
 
    def write_array(array, **kwargs):
        sep = kwargs.get('sep', ' ')
        end = kwargs.get('end', '\n')
        stdout.write(sep.join(str(a) for a in array) + end)
 
    N, Q = [int(x) for x in input().split()]
    updates1 = []
    updates2 = []
    for i in range(N):
        S, T, X = [int(x) for x in input().split()]
        updates1.append((S - X, X))
        updates2.append((T - X, X))
 
    active = []
    to_delete = collections.defaultdict(int)
    import heapq
    heapq.heapify(updates1)
    heapq.heapify(updates2)
    for _ in range(Q):
        x = int(input())
        while updates1 and updates1[0][0] <= x:
            coord, val = heapq.heappop(updates1)
            heapq.heappush(active, val)
 
        while updates2 and updates2[0][0] <= x:
            coord, val = heapq.heappop(updates2)
            to_delete[val] += 1
 
        while active and to_delete[active[0]] > 0:
            to_delete[active[0]] -= 1
            heapq.heappop(active)
        write(active[0] if active else -1)
 
main()
