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 heapq as hq
from collections import defaultdict
N, Q = map(int, input().split())
event = []
for i in range(N):
    si, ti, xi = map(int, input().split())
    event.append([si - xi, ti - xi, xi])
#STX = [list(map(int, input().split())) for i in range(N)]
Dlist = [int(input()) for i in range(Q)]
#for s,t,x in STX:
#    event.append([s - x, t-x, x])
event.sort(key=lambda x:x[0])
h = []
tdic = defaultdict(int)
ind = 0
for Di in Dlist:
    while ind<N and event[ind][0] <= Di:
        #Diまでに始まった工事を追加
        hq.heappush(h, event[ind][2])
        tdic[event[ind][2]] = event[ind][1]
        ind += 1
    while h and Di >= tdic[h[0]]:
        #Diまでに終わった工事を削除
        hq.heappop(h)
    if h:
        print(h[0])
    else:
        print(-1)