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E - Roadwork

Score : $500$ points

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.

4 6
1 3 2
7 13 10
18 20 13
3 4 2
0
1
2
3
5
8

2
2
10
-1
13
-1

The first person starts coordinate $0$ at time $0$ and stops walking at coordinate $2$ when reaching a point blocked by the first roadwork at time $2$.

The second person starts coordinate $0$ at time $1$ and reaches coordinate $2$ at time $3$. The first roadwork has ended, but the fourth roadwork has begun, so this person also stops walking at coordinate $2$.

The fourth and sixth persons encounter no roadworks while walking, so they walk forever. The output for these cases is $-1$.