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 = map(int,input().split())
imos = []
for i in range(n):
    s,t,x = map(int,input().split())
    imos.append((s-x,x))
    imos.append((t-x,-x))
ans = set()
j = 0
for i in range(q):
    d = int(input())
    imos.append((d,1e100))
imos.sort()
m = 1e100
flag = False
for t,stop in imos:
    if stop == 1e100:
        if ans:
            if not flag:
                m = min(ans)
                flag = True
            print(m)
        else:
            print(-1)
    elif stop > 0:
        ans.add(stop)
        if stop < m:
            m = stop
            flag = True
    else:
        ans.remove(-stop)
        if m == -stop:flag = False