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
import sys
input=sys.stdin.readline

N,Q=map(int,input().split())
H=[]
for i in range(N):
    s,t,x=map(int,input().split())
    H.append([s-x,t-x,x])
H.sort()
#print(H)
P=0
q=[]
heapq.heapify(q)
for i in range(Q):
    n=int(input())
    #print("A",len(q))
    if P<N:
        while H[P][0]<=n:
            heapq.heappush(q,[H[P][2],H[P][0],H[P][1]])
            P+=1
            if P==N:
                break
    #print("B",i,len(q))
    if len(q)>0:
        while q[0][2]<=n:
            heapq.heappop(q)
            if len(q)==0:
                break
    if len(q)==0:
        print(-1)
    else:
        print(q[0][0])