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.buffer.readline
import heapq

def main():
    N,Q = map(int,input().split())
    event = []
    
    for _ in range(N):
        s,t,x = map(int,input().split())
        event.append((s-x,1,x))
        event.append((t-x,0,x))
        
    for i in range(Q):
        a = int(input())
        event.append((a,2,i))
    
    event.sort()
    ans = [-1]*Q
    use = set()
    stop = []
    
    for a,b,c in event:
        if b == 1:
            use.add(c)
            heapq.heappush(stop,c)
        elif b == 0:
            use.remove(c)
        else:
            while stop and stop[0] not in use:
                heapq.heappop(stop)
            ans[c] = -1 if len(stop) == 0 else stop[0]
    
    for num in ans:
        print(num)

if __name__ == "__main__":
    main()
