Chunga-Changa
Contest: Codeforces Round 567 (Div. 2)
Difficulty rating: 1000
Tags: greedy, math

Soon after the Chunga-Changa island was discovered, it started to acquire some forms of civilization and even market economy. A new currency arose, colloquially called "chizhik". One has to pay in chizhiks to buy a coconut now.

Sasha and Masha are about to buy some coconuts which are sold at price $$$z$$$ chizhiks per coconut. Sasha has $$$x$$$ chizhiks, Masha has $$$y$$$ chizhiks. Each girl will buy as many coconuts as she can using only her money. This way each girl will buy an integer non-negative number of coconuts.

The girls discussed their plans and found that the total number of coconuts they buy can increase (or decrease) if one of them gives several chizhiks to the other girl. The chizhiks can't be split in parts, so the girls can only exchange with integer number of chizhiks.

Consider the following example. Suppose Sasha has $$$5$$$ chizhiks, Masha has $$$4$$$ chizhiks, and the price for one coconut be $$$3$$$ chizhiks. If the girls don't exchange with chizhiks, they will buy $$$1 + 1 = 2$$$ coconuts. However, if, for example, Masha gives Sasha one chizhik, then Sasha will have $$$6$$$ chizhiks, Masha will have $$$3$$$ chizhiks, and the girls will buy $$$2 + 1 = 3$$$ coconuts.

It is not that easy to live on the island now, so Sasha and Mash want to exchange with chizhiks in such a way that they will buy the maximum possible number of coconuts. Nobody wants to have a debt, so among all possible ways to buy the maximum possible number of coconuts find such a way that minimizes the number of chizhiks one girl gives to the other (it is not important who will be the person giving the chizhiks).

Input format:
The first line contains three integers $$$x$$$, $$$y$$$ and $$$z$$$ ($$$0 \le x, y \le 10^{18}$$$, $$$1 \le z \le 10^{18}$$$) — the number of chizhics Sasha has, the number of chizhics Masha has and the price of a coconut.

Output format:
Print two integers: the maximum possible number of coconuts the girls can buy and the minimum number of chizhiks one girl has to give to the other.

Constraints:
Time limit: 1.0 s
Memory limit: 512.0 MB

Note:
The first example is described in the statement. In the second example the optimal solution is to dot exchange any chizhiks. The girls will buy $$$3 + 4 = 7$$$ coconuts.

Example input:
5 4 3

Example output:
3 1

Example input:
6 8 2

Example output:
7 0

Editorial:
• It's easy to calculate how much coconuts we will buy: $$$k = \lfloor \frac{x + y}{z} \rfloor$$$ (suppose that all money transferred to a single person, this way the number of bought coconuts would be clearly maximal)
• If $$$k = \lfloor \frac{x}{z} \rfloor + \lfloor \frac{y}{z} \rfloor$$$, then the answer is $$$\langle k, 0 \rangle$$$. The remaining case is a bit harder.
• Let's notice, that there is no need to transfer $$$\ge z$$$ chizhiks, since the one transferring money could have used $$$z$$$ chizhiks to buy one more coconut herself.
• Also it's optimal to transfer coins such that the remainder modulo $$$z$$$ of the receiving part will turn to be exactly zero (we could have simply transfer less for the same effect).
• So the answer is $$$\langle k, \min (z - (x \bmod z), z - (y \bmod z)) \rangle$$$.