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
from heapq import heappush, heappop
import sys
input = sys.stdin.readline

N, Q = map(int, input().split())
E = []
for i in range(N):
    s, t, x = map(int, input().split())
    E.append((s - x, t - x, x))

D = []
for i in range(Q):
    d = int(input())
    D.append(d)

E = sorted(E)

que = []

s, t, x = E[0]
j = 1
y, e = N, N
ans = [-1] * Q
for i, d in enumerate(D):
    while j < N + 1 and s <= d:
        heappush(que, (x, t))
        y, e = que[0]
        if j < N:
            s, t, x = E[j]
        j += 1
    while que and e <= d:
        heappop(que)
        if que:
            y, e = que[0]

    if que:
        ans[i] = y

for i in ans:
    print(i)