There are $n$ apples and $m$ bananas, and each of them has an integer weight between $1 \ldots k$ . Your task is to calculate, for each weight $w$ between $2 \dots 2k$ , the number of ways we can choose an apple and a banana whose combined weight is $w$ .
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.
For each integer $w$ between $2 \ldots 2k$ print the number of ways to choose an apple and a banana whose combined weight is $w$ .
5 3 4 5 2 5 4 3 2 3· · \n · · \n · · · \n
0 0 1 2 1 2 4 2 0· · · · · · · · \n
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.