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
#ref : https://atcoder.jp/contests/abc128/submissions/5694292
#工事を座標順に処理，工事にぶつかる人をにぶたん
#すでに更新済みだったら更新しない．-> jumpで管理
from bisect import bisect_left
N, Q = map(int, input().split())
consts = []
for _ in range(N):
    s,t,x = map(int, input().split())
    consts.append((x,s,t))
consts.sort()
D=[int(input()) for _ in range(Q)]
ans=[-1]*Q
jump=[-1]*Q
for x,s,t in consts:
    left=bisect_left(D,s-x)
    right=bisect_left(D,t-x)
    while left<right:
        if jump[left]==-1:
            ans[left]=x
            jump[left]=right
            left += 1
        else:
            left=jump[left]
print(*ans, sep='\n')