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
n,q=[int(j) for j in input().split()]
l=[]
for i in range(n):
    s,t,x=[int(j) for j in input().split()]
    l.append((s-x,1,x))
    l.append((t-x,0,x))

for i in range(q):
    d=int(input())
    l.append((d,2,i))

l.sort()

ans=[-1]*q
ll=set()
m=10**18
p=False
for i,j,x in l:
    if j==1:
        ll.add(x)
        if m>x:
            m=x
            p=True
    elif j==0:
        ll.remove(x)
        if x==m:
            p=False
    else:
        if not p:
            if ll:
                p=True
                m=min(ll)
            else:
                m=-1
        ans[x]=m
print('\n'.join(map(str,ans)))

