Problem R
Maximally Unfair Fair IKEA Trip

Image from Wikimedia.org

Dagur and his friends were in IKEA buying furniture for the Faulty Komputerprogram (FK) club, but Dagur is lazy and does not want to carry furniture all the way back. But everyone has to carry the same number of items, otherwise it would be unfair. Therefore, Dagur has decided to carry as little weight as possible.

You are given $k$, the number of people carrying stuff (Dagur and his friends), and a list of $n$ furniture items and their weights. Find what items Dagur should carry to minimise weight.

Note that the number of people does not necessarily divide the number of goods, so not everyone can carry the same number of items. If this is the case Dagur will try to take as few items as possible, as long as it does not make it too obvious he’s trying to get away lightly.

Dagur will try to get away with taking only $\lfloor n/k \rfloor $ items. The only exception is when this would make his laziness obvious. This happens when the lightest $\lceil n/k \rceil $ items are strictly lighter than the next $\lfloor n/k \rfloor $ items, when they are ordered by weight. In this case Dagur will take $\lceil n/k \rceil $ items to make things less obvious.

Let us take an example with $7$ items and $3$ people carrying, that is to say $n = 7$ and $k = 3$. Call the items $x_1, x_2, \ldots , x_{7}$ after putting them in increasing weight order, so $x_1 < x_2 < \cdots < x_{7}$. Then Dagur will take $2$ items, unless if $x_1 + x_2 + x_3 < x_4 + x_5$, then he will take $3$ items instead.

If there are multiple different lightest sets of items that Dagur can take, Dagur breaks ties by taking the items that appeared earliest in the list of bought items.

Input

Input consists of multiple lines. The first line contains a single integer $k$, the number of people carrying items. The next line contains a single integer $n$, the number of products purchased at IKEA. The next line contains $n$ lines, the list of all bought products, each line containing the name of one product and its weight. Each weight is at most $100\, 000$. Each name is at most 10 English letters and has no spaces, names are also not empty.

Output

On the first line, write the total weight that Dagur carries on his shoulders. The next lines should contain all the items that Dagur carries on his shoulders in alphabetical order, one per line.

Scoring

2
2
EKET 123
VINTERFINT 234

123
EKET

1
2
VINTERFINT 234
EKET 123

357
EKET
VINTERFINT

3
7
SILKESTRAD 124
VINTERFINT 21
EKET 12432
BERGGRAN 9283
BUSKBJORK 12
KLOKHET 2
TUVKORNEL 1

15
BUSKBJORK
KLOKHET
TUVKORNEL