Apples and Bananas

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.

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.