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
N,Q = map(int,input().split())
STX = [tuple(map(int,input().split())) for i in range(N)]
D = [int(input()) for i in range(Q)]

starts = []
ends = []
for i,(s,t,x) in enumerate(STX):
    starts.append((s-x,i))
    ends.append((t-x,i))
starts.sort(key=lambda x:x[0], reverse=True)
ends.sort(key=lambda x:x[0], reverse=True)

import heapq
hq = []
heapq.heapify(hq)
delset = set()

ans = []
for d in D:
    while starts and starts[-1][0] <= d:
        _,i = starts.pop()
        x = STX[i][2]
        heapq.heappush(hq, x*N+i)
    while ends and ends[-1][0] <= d:
        _,i = ends.pop()
        delset.add(i)
    while hq:
        i = hq[0]%N
        if i in delset:
            heapq.heappop(hq)
        else:
            break
    if len(hq)==0:
        ans.append(-1)
    else:
        ans.append(hq[0]//N)

print(*ans, sep='\n')