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
from collections import deque, defaultdict
import copy
import bisect
input=sys.stdin.readline
sys.setrecursionlimit(10 ** 9)


N, Q = list(map(int, input().split()))
STX=[]
D=[]
for i in range(N):
    S, T, X = list(map(int, input().split()))
    STX.append((X, S, T))
STX = sorted(STX, key=lambda x: x[0])

for i in range(Q):
    D.append(int(input()))

skip = [-1]*Q

dist = [-1]*Q

for X, S, T in STX:
    s = S - X
    t = T - X - 1
    a = bisect.bisect_left(D, s)
    b = bisect.bisect_right(D, t)
    #print(D)
    j = a
    while j < b:
        if skip[j] == -1:
            skip[j] = b
            dist[j] = X
            j+=1
        else:
            j=skip[j]


for i in range(Q):
    print(dist[i])