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