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
from bisect import bisect,bisect_left
import sys
input=sys.stdin.readline

def main():
    n,q=map(int,input().split())
    xst=[]
    for i in range(n):
        s,t,x=map(int,input().split())
        xst.append([x,s-x,t-x])
    xst.sort()
    d=[None]*q
    for i in range(q):
        d[i]=int(input())
    ans=[-1]*q
    skip=[-1]*q
    for u in xst:
        x ,left ,right = u
        a=bisect_left(d,left)
        b=bisect_left(d,right)
        while a < b:
            if skip[a] == -1:
                ans[a]=x
                skip[a]=b
                a+=1
            else:
                a=skip[a]
    for u in ans:
        print(u)

if __name__=="__main__":
    main()