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 heapq import heappop,heappush
from bisect import bisect,bisect_left
N,Q=map(int,input().split())
table=[]
for i in range(N):
    s,t,x=map(int,input().split())
    #print((max(0,s-x),t-1-x))
    table.append((x,s-x,t-x))
H=[]
D=[int(input()) for i in range(Q)]
#print(D)
for x,a,b in table:
    #print(x,a,b,(x,bisect_left(D,a),bisect(D,b)))
    heappush(H,(bisect_left(D,a),bisect_left(D,b),x))
#print(H)
K=[]
U=[10**12]*Q
J=[]
for i in range(Q):
    while len(H)>0 and H[0][0]<=i:
        a,b,x=heappop(H)
        heappush(J,(x,a,b))
    while len(J)>0 and J[0][2]<=i:
        y,u,v=heappop(J)
    if len(J)>0 and J[0][1]<=i<J[0][2]:
        U[i]=J[0][0]
    #print(i,J,H,U[i])
for i in range(Q):
    if U[i]==10**12:
        print(-1)
    else:
        print(U[i])
