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
from heapq import heappush, heappop


I = sys.stdin.readlines()
N, Q = map(int, I[0].split())
P = []
for i in range(1, N + 1):
    s, t, x = map(int, I[i].split())
    P.append((s - x, t - 1 - x, x))
P.sort()


q = []
cur = 0
for i in range(N + 1, N + Q + 1):
    d = int(I[i])
    while cur < N and P[cur][0] <= d:
        s, t, x = P[cur]
        heappush(q, (x, t))
        cur += 1
    ans = -1
    while len(q) > 0:
        x, t = q[0]
        if d <= t:
            ans = x
            break
        else:
            heappop(q)
    print(ans)

