The size of the hash table is not determinate at the very beginning. If the total size of keys is too large (e.g. size >= capacity / 10), we should double the size of the hash table and rehash every keys. Say you have a hash table looks like below:

``````size=3, capacity=4

[null, 21, 14, null]
↓    ↓
9   null
↓
null
``````

The hash function is:

``````int hashcode(int key, int capacity) {
return key % capacity;
}
``````

Here we have three numbers, `9`, `14` and `21`, where `21` and `9` share the same position as they all have the same hashcode `1` (21 % 4 = 9 % 4 = 1). We store them in the hash table by linked list.

Rehashing this hash table, double the capacity, you will get:

``````size=3, capacity=8

index:   0    1    2    3     4    5    6   7
hash : [null, 9, null, null, null, 21, 14, null]
``````

For this problem, given the original hash table, return the new hash table after rehashing.

Notice

For negative integer in hash table, the position can be calculated as follow:

C++/Java: if you directly calculate `-4 % 3` you will get `-1`. You can use function: `a % b = (a % b + b) % b` to make it is a non negative integer. Python: you can directly use `-1 % 3`, you will get `2` automatically.

Example

``````Original Table:

[null, 21, 14, null]
↓    ↓
9   null
↓
null

Rehashed Table:

[null, 9, null, null, null, 21, 14, null]
↓                    ↓    ↓
null                 null null

``````