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
import bisect
from heapq import heappop, heappush, heapify
input = sys.stdin.readline
from itertools import chain
sys.setrecursionlimit(10**9)
N,Q= map(int,input().split())
STX = [list(map(int,input().split())) for i in range(N)]
D = [int(input()) for i in range(Q)]

inf = 10**15
TEMP = [[(s-x,True,x),(t-x,False,x)] for s,t,x in STX] + [[(-inf,True,inf),(inf,False,inf)]]
PFX = sorted(list(chain(*TEMP)))

addq = [inf]
delq = [inf+1]
D.append(inf)
iterD = iter(D)

d = next(iterD)
for p,f,x in PFX:
    while d < p:
        ans = addq[0] if not addq[0] == inf else -1
        print(ans)
        d = next(iterD)
        if d == inf:
            exit()
    if f:
        heappush(addq, x)
    else:
        heappush(delq, x)
    while addq[0] == delq[0]:
        heappop(addq)
        heappop(delq)




