#P1859D. Andrey and Escape from Capygrad

    ID: 8599 Type: RemoteJudge 2000ms 256MiB Tried: 0 Accepted: 0 Difficulty: 6 Uploaded By: Tags>binary searchdata structuresdpdsugreedysortings*1800

Andrey and Escape from Capygrad

No submission language available for this problem.

Description

An incident occurred in Capygrad, the capital of Tyagoland, where all the capybaras in the city went crazy and started throwing mandarins. Andrey was forced to escape from the city as far as possible, using portals.

Tyagoland is represented by a number line, and the city of Capygrad is located at point 00. There are nn portals all over Tyagoland, each of which is characterised by four integers lil_i, rir_i, aia_i and bib_i (1liaibiri1091 \le l_i \le a_i \le b_i \le r_i \le 10^9). Note that the segment [ai,bi][a_i, b_i] is contained in the segment [li,ri][l_i, r_i].

If Andrey is on the segment [li,ri][l_i, r_i], then the portal can teleport him to any point on the segment [ai,bi][a_i, b_i]. Andrey has a pass that allows him to use the portals an unlimited number of times.

Andrey thinks that the point xx is on the segment [l,r][l, r] if the inequality lxrl \le x \le r is satisfied.

Andrey has qq options for where to start his escape, each option is characterized by a single integer xix_i — the starting position of the escape. He wants to escape from Capygrad as far as possible (to the point with the maximum possible coordinate). Help Andrey determine how far he could escape from Capygrad, starting at each of the qq positions.

Each test consists of multiple test cases. The first line contains a single integer tt (1t1041 \le t \le 10^4) — the number of sets of test cases. The description of test cases follows.

The first line of each test case contains a single integer nn (1n21051 \le n \le 2 \cdot 10^5) — the number of portals.

Each of the next nn lines contains four integers lil_i, rir_i, aia_i, and bib_i (1liaibiri109)(1 \le l_i \le a_i \le b_i \le r_i \le 10^9) — the characteristics of the portals.

The next line contains a single integer qq (1q21051 \le q \le 2 \cdot 10^5) — the number of positions.

The following line contains qq integers x1,x2,,xqx_1, x_2, \ldots, x_q (1xi1091 \le x_i \le 10^9) — the position from which Andrey will start his escape in the ii-th options.

It is guaranteed that the sum of nn and the sum of qq over all test cases does not exceed 21052 \cdot 10^5.

For each test case, output a single line of qq integers, containing the answers to Andrey's questions.

Input

Each test consists of multiple test cases. The first line contains a single integer tt (1t1041 \le t \le 10^4) — the number of sets of test cases. The description of test cases follows.

The first line of each test case contains a single integer nn (1n21051 \le n \le 2 \cdot 10^5) — the number of portals.

Each of the next nn lines contains four integers lil_i, rir_i, aia_i, and bib_i (1liaibiri109)(1 \le l_i \le a_i \le b_i \le r_i \le 10^9) — the characteristics of the portals.

The next line contains a single integer qq (1q21051 \le q \le 2 \cdot 10^5) — the number of positions.

The following line contains qq integers x1,x2,,xqx_1, x_2, \ldots, x_q (1xi1091 \le x_i \le 10^9) — the position from which Andrey will start his escape in the ii-th options.

It is guaranteed that the sum of nn and the sum of qq over all test cases does not exceed 21052 \cdot 10^5.

Output

For each test case, output a single line of qq integers, containing the answers to Andrey's questions.

Sample Input 1

5
3
6 17 7 14
1 12 3 8
16 24 20 22
6
10 2 23 15 28 18
3
3 14 7 10
16 24 20 22
1 16 3 14
9
2 4 6 8 18 23 11 13 15
2
1 4 2 3
3 9 6 7
3
4 8 1
5
18 24 18 24
1 8 2 4
11 16 14 14
26 32 28 30
5 10 6 8
9
15 14 13 27 22 17 31 1 7
6
9 22 14 20
11 26 13 24
21 33 22 23
21 33 25 32
1 6 3 4
18 29 20 21
8
11 23 16 5 8 33 2 21

Sample Output 1

14 14 23 15 28 22 
14 14 14 14 22 23 14 14 15 
7 8 7 
15 14 14 30 24 17 31 4 8 
32 32 32 5 8 33 4 32

Note

In the first test case:

Optimal actions when starting from each position:

  1. Use portal 11 and teleport to point b1=14b_1 = 14.
  2. Use portal 22 first and teleport to point 66, which is on the segment [l1,r1]=[6,17][l_1, r_1] = [6, 17], then use portal 11 and teleport to point b1=14b_1 = 14.
  3. Stay at point x3=23x_3=23 without using any portals.
  4. Stay at point x4=15x_4=15 without using any portals.
  5. Point x5=28x_5=28 is not on any segment, so Andrey won't be able to teleport anywhere.
  6. Point x6=18x_6=18 is only on the segment [l3,r3]=[16,24][l_3, r_3] = [16, 24], use portal 33 and teleport to point b3=22b_3 = 22.

In the fifth test case:

Optimal actions when starting from each position:

  1. Use portal 11 first and teleport to point 1515 on the segment [a1,b1]=[14,20][a_1, b_1] = [14, 20], then use portal 22 and teleport to point 2121, which is on the segment [l4,r4]=[21,33][l_4, r_4] = [21, 33] and on the segment [a2,b2]=[13,24][a_2, b_2] = [13, 24], then teleport to point b4=32b_4 = 32.
  2. Use portal 66 first and teleport to point 2020 on the segment [a6,b6]=[20,21][a_6, b_6] = [20, 21], then use portal 22 and teleport to point 2222, which is simultaneously on the segment [l4,r4]=[21,33][l_4, r_4] = [21, 33] and on the segment [a2,b2]=[13,24][a_2, b_2] = [13, 24], then teleport to point b4=32b_4 = 32.
  3. Perform the same actions as from the first position.
  4. Stay at point x4=5x_4=5 without using any portals.
  5. Point 88 is not on any segment, so Andrey won't be able to teleport anywhere.
  6. Stay at point x6=33x_6=33 without using any portals.
  7. Use portal 55 and teleport to point b5=4b_5 = 4.
  8. Perform the same actions as from the first position.