Roadwork

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

inputFormat

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

outputFormat

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

样例

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

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