**Time limit:**1.00 s**Memory limit:**512 MB

**Input**

The first input line contains three integers $k$, $n$ and $m$: the number $k$, the number of apples and the number of bananas.

The next line contains $n$ integers $a_1,a_2,\ldots,a_n$: weight of each apple.

The last line contains $m$ integers $b_1,b_2,\ldots,b_m$: weight of each banana.

**Output**

For each integer $w$ between $2 \ldots 2k$ print the number of ways to choose an apple and a banana whose combined weight is $w$.

**Constraints**

- $1 \le k,n,m \le 2 \cdot 10^5$

- $1 \le a_i \le k$

- $1 \le b_i \le k$

**Example**

Input:

`5 3 4`

5 2 5

4 3 2 3

Output:

`0 0 1 2 1 2 4 2 0 `

Explanation: For example for $w$ = $8$ there are $4$ different ways: we can pick an apple of weight $5$ in two different ways and a banana of weight $3$ in two different ways.