p03033 AtCoder Beginner Contest 128 - Roadwork
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
```python
from collections import deque, defaultdict
from heapq import heappush, heappop
import sys
input = sys.stdin.readline

N, Q = map(int, input().split())
events = [None] * (2*N)
for i in range(N):
    S, T, X = map(int, input().split())
    events[2*i] = (S-X, X)
    events[2*i+1] = (T-X, -X)
events.sort(key=lambda x: x[0])
events = deque(events)
ans = [0] * Q
cur = []
remove = defaultdict(int)
for i in range(Q):
    D = int(input())
    while events and events[0][0] <= D:
        t, x = events.popleft()
        if x > 0:
            heappush(cur, x)
        else:
            remove[-x] += 1
    while cur and remove[cur[0]]:
        remove[cur[0]] -= 1
        heappop(cur)
    ans[i] = cur[0] if cur else -1
print(*ans, sep='\n')

```