D. Berserk Monsters
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

Monocarp is playing a computer game (yet again). Guess what is he doing? That's right, killing monsters.

There are $$$n$$$ monsters in a row, numbered from $$$1$$$ to $$$n$$$. The $$$i$$$-th monster has two parameters: attack value equal to $$$a_i$$$ and defense value equal to $$$d_i$$$. In order to kill these monsters, Monocarp put a berserk spell on them, so they're attacking each other instead of Monocarp's character.

The fight consists of $$$n$$$ rounds. Every round, the following happens:

  • first, every alive monster $$$i$$$ deals $$$a_i$$$ damage to the closest alive monster to the left (if it exists) and the closest alive monster to the right (if it exists);
  • then, every alive monster $$$j$$$ which received more than $$$d_j$$$ damage during this round dies. I. e. the $$$j$$$-th monster dies if and only if its defense value $$$d_j$$$ is strictly less than the total damage it received this round.

For each round, calculate the number of monsters that will die during that round.

Input

The first line contains one integer $$$t$$$ ($$$1 \le t \le 10^4$$$) — the number of test cases.

Each test case consists of three lines:

  • the first line contains one integer $$$n$$$ ($$$1 \le n \le 3 \cdot 10^5$$$);
  • the second line contains $$$n$$$ integers $$$a_1, a_2, \dots, a_n$$$ ($$$1 \le a_i \le 10^9$$$);
  • the third line contains $$$n$$$ integers $$$d_1, d_2, \dots, d_n$$$ ($$$1 \le d_i \le 10^9$$$).

Additional constraint on the input: the sum of $$$n$$$ over all test cases does not exceed $$$3 \cdot 10^5$$$.

Output

For each test case, print $$$n$$$ integers. The $$$i$$$-th integer should be equal to the number of monsters that die during the $$$i$$$-th round.

Example
Input
3
5
3 4 7 5 10
4 9 1 18 1
2
2 1
1 3
4
1 1 2 4
3 3 4 2
Output
3 1 0 0 0 
0 0 
1 1 1 0
Note

Explanation for the first test case of the example:

During the first round, the following happens:

  • the monster $$$1$$$ deals $$$3$$$ damage to the monster $$$2$$$;
  • the monster $$$2$$$ deals $$$4$$$ damage to the monster $$$1$$$ and the monster $$$3$$$;
  • the monster $$$3$$$ deals $$$7$$$ damage to the monster $$$2$$$ and the monster $$$4$$$;
  • the monster $$$4$$$ deals $$$5$$$ damage to the monster $$$3$$$ and the monster $$$5$$$;
  • the monster $$$5$$$ deals $$$10$$$ damage to the monster $$$4$$$;
  • the monster $$$1$$$ does not die, since it received $$$4$$$ damage and its defense is $$$4$$$;
  • the monster $$$2$$$ dies, since it received $$$10$$$ damage and its defense is $$$9$$$;
  • the monster $$$3$$$ dies, since it received $$$9$$$ damage and its defense is $$$1$$$;
  • the monster $$$4$$$ does not die, since it received $$$17$$$ damage and its defense is $$$18$$$;
  • the monster $$$5$$$ dies, since it received $$$5$$$ damage and its defense is $$$1$$$.

After the first round, the monsters $$$1$$$ and $$$4$$$ stay alive.

During the second round, the following happens:

  • the monster $$$1$$$ deals $$$3$$$ damage to the monster $$$4$$$;
  • the monster $$$4$$$ deals $$$5$$$ damage to the monster $$$1$$$;
  • the monster $$$1$$$ dies, since it received $$$5$$$ damage and its defense is $$$4$$$;
  • the monster $$$4$$$ does not die, since it received $$$3$$$ damage and its defense is $$$18$$$.

During the next three rounds, only the $$$4$$$-th monster is alive, so nothing happens.