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())
S = [list(map(int,input().split())) for i in range(n)]
D = [int(input()) for i in range(q)]

A = []
for i in range(n):
    s = S[i][0]
    t = S[i][1]
    x = S[i][2]
    A.append([s-x-0.5, x, i, 0])
    A.append([t-x-0.5, x, i, 1])
for i in range(q):
    A.append([D[i], 0, 0, 2])

A.sort()
from heapq import heappop, heappush
Q = []
F = [0] * n
for i in range(len(A)):
    s = A[i][0]
    x = A[i][1]
    j = A[i][2]
    f = A[i][3]
    if f == 0:
        heappush(Q, [x, j])
        F[j] = 1
    elif f == 1:
        F[j] = 0
    elif f == 2:
        while len(Q) > 0 and F[Q[0][1]] == 0:
            heappop(Q)
        if len(Q) > 0:
            print(Q[0][0])
        else:
            print(-1)
