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

import heapq
N, Q = (int(i) for i in input().split())
L = [0] * (2 * N + Q)
for i in range(N):
    S, T, X = (int(i) for i in input().split())
    L[2 * i] = (S-X, 1, X)
    L[2 * i + 1] = (T-X, -1, X)
for i in range(Q):
    D = int(input())
    L[2 * N + i] = (D, 2, 0)
L.sort()

Xs = set([])
XH = []
heapq.heapify(XH)
for t, f, X in L:
    if f == 1:
        Xs.add(X)
        heapq.heappush(XH, X)
    elif  f == -1:
        Xs.remove(X)
    else:
        if Xs:
            while XH[0] not in Xs:
                X = heapq.heappop(XH)
            print(XH[0])
        else:
            print("-1")