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
input = sys.stdin.readline
n,Q=map(int,input().split())
b_num = 2**(n-1).bit_length()
mx = 10**9
segl=[mx]*2*b_num 
def update(k, x):
    k += b_num-1
    segl[k] = x
    while k+1:
        k = (k-1)//2
        segl[k] = min(segl[k*2+1],segl[k*2+2])
if __name__ == '__main__':
    xs = []
    for i in range(n):
        s,t,x=map(int,input().split())
        xs += [(s-x,True,x,i), (t-x,False,x,i)]
    qs = []
    for _ in range(Q):
        qs.append(int(input()))
    xs.sort(key=lambda x:x[0])
    j = 0
    for x in xs:
        while Q-j:
            if qs[j] < x[0]:
                print(segl[0] if segl[0]!= mx else -1)
                j += 1
                continue
            break
        update(x[3], x[2] if x[1] else mx)
    while Q-j:
        print(-1)
        j+=1
