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
def N(): return int(input())
def NM():return map(int,input().split())
def L():return list(NM())
def LN(n):return [N() for i in range(n)]
def LL(n):return [L() for i in range(n)]
def YesNo(x):print("Yes")if x==True else print("No")
n,q=NM()
l=[]
for i in range(n):
    s,t,x=NM()
    l.append((s-x,t-x,x))
l.sort()
INF=float("inf")
l+=[(INF,INF,INF)]
d=LN(q)
q=[]
from heapq import heappush,heappop
j=0
for i in d:
    while l[j][0]<=i:
        s,t,x=l[j]
        heappush(q,(x,t))
        j+=1
    if len(q)==0:
        print(-1)
    else:
        while q:
            x,t=heappop(q)
            if t>i:
                heappush(q,(x,t))
                print(x)
                break
        else:
            print(-1)