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 bisect

def solve():
    N, Q = [int(_) for _ in raw_input().split()]
    STX = []
    for i in range(N):
        Si, Ti, Xi = [int(_) for _ in raw_input().split()]
        STX.append((Si - Xi, Ti - Xi, Xi))
    D = []
    for i in range(Q):
        D.append((int(raw_input()), i))
    STX.sort(key = lambda x:x[2])
    # D have already been sorted based on settings on problem
    ans = [-1] * Q
    l = [None] * Q
    for i in range(N):
        Li, Ri, Xi = STX[i]
        lit = bisect.bisect_left(D, (Li, -1))
        rit = bisect.bisect_left(D, (Ri, -1))
        while lit < rit:
            if l[lit] is not None:
                lit = l[lit]
            else:
                ans[D[lit][1]] = Xi
                l[lit] = rit
                lit += 1
    for i in range(Q):
        print ans[i]

if __name__ == '__main__':
    solve()
