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
from bisect import bisect_left
inf = float('inf')

N, Q = map(int,input().split())
STX = [list(map(int,input().split())) for _ in range(N)]
D = [int(input()) for _ in range(Q)]

res = 1
while res < Q:
    res <<= 1
N0 = res
data = [inf for _ in range(2*N0-1)]

def update(l, r, x):
    L = l + N0
    R = r + N0
    while L < R:
        if R & 1:
            R -= 1
            data[R] = min(data[R], x)
        if L & 1:
            data[L] = min(data[L], x)
            L += 1
        L >>= 1; R >>= 1

def value(k):
    k += N0
    res = data[k]
    while k != 0:
        k >>= 1
        res = min(res, data[k])
    return res


for S, T, X in STX:
    l = bisect_left(D, S-X)
    r = bisect_left(D, T-X)
    update(l, r, X)

for k in range(Q):
    ans = value(k)
    if ans == inf:
        ans = -1
    print(ans)