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
import heapq
n,q=map(int,input().split())
l=[list(map(int,input().split())) for i in range(n)]
L1=[]
for i in range(n):
  L1.append((l[i][0]-l[i][2],1,l[i][2]))
  L1.append((l[i][1]-l[i][2],-1,l[i][2]))
for i in range(q):
  L1.append((int(input()),2,0))
L1.sort()
L2=[]
heapq.heapify(L2)
L3=[]
L3=set(L3)
for i in range(len(L1)):
  if L1[i][1]==1:
    heapq.heappush(L2,L1[i][2])
    L3.add(L1[i][2])
  elif L1[i][1]==-1:
    L3.remove(L1[i][2])
  else:
    while L2 and L2[0] not in L3:
      heapq.heappop(L2)
    if L2:
      print(L2[0])
    else:
      print(-1)