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
N,Q=map(int,input().split())
import sys
def input(): return sys.stdin.readline().strip()
STX=[list(map(int,input().split())) for i in range(N)]
D=[int(input()) for i in range(Q)]
X=[]
for s,t,x in STX:
    X.append((s-x,1,x))
    X.append((t-x,-1,x))
X.sort(key=lambda x:x[0])
a=0
k=[]
from heapq import heappop,heappush
kd={}
for x in X:
    while a<Q and D[a]<x[0]:
        if len(k)>0:
            print(k[0])
        else:
            print(-1)
        a+=1
    if x[1]==1:
        heappush(k,x[2])
        if x[2] in kd:
            kd[x[2]]=0
    else:
        kd[x[2]]=1
        while len(k)>0 and k[0] in kd and kd[k[0]]==1:
            heappop(k)
while a<Q:
    print(-1)
    a+=1