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, heapq
input = sys.stdin.buffer.readline # 入出力高速化

def main():
    N, Q = map(int, input().split())
    tl = [] # イベントタイムライン
    for _ in range(N):
        S, T, X = map(int, input().split())
        tl.append((S-X, 1, X)) # insert
        tl.append((T-X, 0, X)) # erase
    for _ in range(Q):
        D = int(input())
        tl.append((D, 2, 0)) # min
    tl.sort()
    working = list() # 工事中
    todelete = list() # 削除用
    for t, c, x in tl:
        if c == 0: # erase
            heapq.heappush(todelete, x)
        elif c == 1: # insert
            heapq.heappush(working, x)
        else: # min
            while todelete and todelete[0] == working[0]:
                heapq.heappop(todelete)
                heapq.heappop(working)
            print(-1 if not working else working[0])
    return
    
if __name__ == "__main__":
    main()
