### Croatian Olympiad in Informatics 2009

## Task IZBORI

It is election time. V voters attend the election, each casting their vote for one of N political parties. M officials will be elected into the parliament.

The conversion from votes to parliament seats is done using the D'Hondt method with a 5% threshold. More precisely, suppose that the parties are numbered 1 through N and that they receive V1, V2, ..., VN votes. Parliament seats are allocated as follows:

- All parties that receive strictly less than 5% of V votes are erased from the list of parties.
- The parliament is initially empty i.e. every party has zero seats allocated.
- For each party P, the quotient QP=VP/(SP+1) is calculated, where VP is the total number of votes received by party P, and SP is the number of seats already allocated to party P.
- The party with the largest quotient QP is allocated one seat. If multiple parties have the same largest quotient, the lower numbered party wins the seat.
- Repeat steps 3 and 4 until the parliament is full.

The votes are being counted and only part of the V votes has been tallied. It is known how many votes each party has received so far. Write a program that calculates for each party, among all possible outcomes of the election after all V votes are counted, the largest and smallest number of seats the party wins.

### Input

The first line contains the integers V, N and M (1 ≤ V ≤ 10,000,000, 1 ≤ N ≤ 100, 1 ≤ M ≤ 200), the
numbers of votes, parties and seats in the parliament.

The second line contains N integers – how many votes (of those that have been counted) each party
got. The sum of these numbers will be at most V.

### Output

On the first line output N integers separated by spaces – the largest number of seats each party can
win.

On the second line output N integers separated by spaces – the smallest number of seats each party can
win.

### Examples

## Sample Input20 4 5 4 3 6 1 ## Sample Output3 3 3 2 1 0 1 0 |
## Sample Input100 3 5 30 20 10 ## Sample Output4 3 3 1 1 0 |

**In the first example**, 14 votes have been tallied and 6 are yet to be counted. To illustrate one possible outcome, suppose that the first party receives 2 of those 6 votes, the second none, the third 1 vote and the fourth 3 votes. The parties' totals are 6, 3, 7 and 4 votes. All parties exceeded the 5% threshold.

Seats are allocated as follows:

- The quotients are initially 6/1, 3/1, 7/1 and 4/1; the largest is 7/1 so party 3 wins a seat.
- The quotients are 6/1, 3/1, 7/2 and 4/1; the largest is 6/1 so party 1 wins a seat.
- The quotients are 6/2, 3/1, 7/2 and 4/1; the largest is 4/1 so party 4 wins a seat.
- The quotients are 6/2, 3/1, 7/2 and 4/2; the largest is 7/2 so party 3 wins a seat.
- The quotients are 6/2, 3/1, 7/3 and 4/2; parties 1 and 2 are tied with quotients 6/2 and 3/1, but party 1 is lower numbered so it wins the last seat.

In this outcome, the numbers of seats won by the parties are 2, 0, 2 and 1. Since it is possible for the second party not to win any seats, the second number on the second line of output is zero.

All Submissions

Best Solutions

**Point Value:** 30

**Time Limit:** 1.00s

**Memory Limit:** 128M

**Added:** Apr 26, 2009

**Languages Allowed:**

C++03, PAS, C, HASK, ASM, RUBY, PYTH2, JAVA, PHP, SCM, CAML, PERL, C#, C++11, PYTH3

## Comments (Search)

It's quiet in here...