Books

You have been working at the library for quite some time, and you have formed your own impression of each of the $n$ books — $a_i$. The impression is expressed by an integer, the larger the better your impression of the book. Books also have their true interest — $b_i$. You want to read exactly $k$ books. For each book you read, you get $b_i-a_i$ satisfaction, and if you don't read the book, you will regret it for a long time, and your satisfaction will decrease by $b_i-a_i$. Find the maximum level of satisfaction you can get if you have to read exactly $k$ books.

Input

The first line contains two integers $n$ and $k$ ($1\le n\le 10^5$, $0\le k\le n$) — the number of available books and the number of books to be read.

The second line contains $n$ integers $a_i$ ($-10^9\le a_i\le 10^9$) — impressions of the books.

The third line contains $n$ integers $b_i$ ($-10^9\le b_i\le 10^9$) — genuine interest in the books.

Output

In the first line, output a single integer — the maximum satisfaction you can get by reading $k$ books.

In the second line, output $k$ integers from $0$ to $n$ — the numbers of the books you need to read to achieve this satisfaction. If there are several sets that give the maximum satisfaction, output any of them.

Examples

Scoring

The score for each test is divided into two components:

• $50\%$ of the score if the correct maximum satisfaction was found.

• $50\%$ of the score if the set of books to be read was correctly found.

The score for a test is the sum of these two components.

Note that if you want to get a partial score for a test, you still need to follow the output format. That is, output a single integer in the first line — the value of the maximum satisfaction, and $k$ integers in the second line. You can, for example, output $k$ zeros.