Problem Statement

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.