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 = [None] * N
T = [None] * N
X = [None] * N
for i in range(N):
    S[i], T[i], X[i] = map(int, input().split())

D = [None] * Q
for i in range(Q):
    D[i] = int(input())
    
# X S T
roadworks = [(x, s, t) for x, s, t in zip(X, S, T)]
roadworks = sorted(roadworks, key=lambda x: x[0])
#print(roadworks)

# Dは入力時点でソート済み
walkers = D[:]
ans = [-1] * Q
skip = [-1] * Q

import bisect
for x, s, t in roadworks:
    left = bisect.bisect_left(walkers, s - x)
    right = bisect.bisect_left(walkers, t - x)
    
    i = left
    while i < right:
        if skip[i] == -1:
            ans[i] = x
            skip[i] = right
            i += 1
        else:
            i = skip[i]

    
#print(walkers)
for a in ans:
    print(a)
    




    
    
