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.readline
from collections import deque
from heapq import heappush,heappop
import re

def int_raw():
    return int(input())
 
def ss_raw():
    return input().split()
 
def ints_raw():
    return tuple(map(int, ss_raw()))


def main():
    N ,Q = ints_raw()
    origST = []

    for idx  in range(N):
        S,T,X = ints_raw()
        origST.append([S-X,T-X,X])
    Ds = [int(input()) for _ in range(Q)]

    origST.sort()
    stidx = 0
    cur_set = []
    for q in Ds:

        while stidx < len(origST):
            st = origST[stidx]
            if st[0] > q:
                break
            heappush(cur_set,(st[2],st[1]))
            stidx+=1
        while cur_set and cur_set[0][1] <=q:
            heappop(cur_set)
        if len(cur_set)==0:
            print(-1)
        else:
            print(cur_set[0][0])
main()
