Problem:
Score : 200 points

Problem Statement

In the beginning, Takahashi has A cookies, and Aoki has B cookies.
They will perform the following operation alternately, starting from Takahashi:

If the number of cookies in his hand is odd, eat one of those cookies; if the number is even, do nothing. Then, give one-half of the cookies in his hand to the other person.

Find the numbers of cookies Takahashi and Aoki respectively have after performing K operations in total.

Constraints

1 \leq A,B \leq 10^9

1 \leq K \leq 100

A,B and K are integers.

Input

Input is given from Standard Input in the following format:

A B K

Output

Print the number of cookies Takahashi has, and the number of cookies Aoki has, in this order, after performing K operations in total.

Sample Input 1

5 4 2

Sample Output 1

5 3

The process will go as follows:

In the beginning, Takahashi and Aoki have 5 and 4 cookies, respectively.

Takahashi eats one cookie and gives two cookies to Aoki. They now have 2 and 6 cookies, respectively.

Aoki gives three cookies to Takahashi. They now have 5 and 3 cookies, respectively.

Sample Input 2

3 3 3

Sample Output 2

1 3

Sample Input 3

314159265 358979323 84

Sample Output 3

448759046 224379523

Solution in C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <algorithm>
#include <cmath>
#include <deque>
#include <iomanip>
#include <iostream>
#include <map>
#include <numeric>
#include <set>
#include <string>
#include <vector>

using namespace std;
using LLONG = long long;
const LLONG MOD = 1000000007;

int main()
{
    // 操作回数がK<=100なのでシミュレーションで間に合う
    vector<int> cookies(2);
    int K;
    cin >> cookies[0] >> cookies[1] >> K;
    for (int i = 0; i < K; ++i)
    {
        int first = i % 2 == 0 ? 0 : 1;
        int second = i % 2 == 0 ? 1 : 0;
        if (cookies[first] % 2 == 1) --cookies[first];
        cookies[first] /= 2;
        cookies[second] += cookies[first];
    }
    cout << cookies[0] << ' ' << cookies[1] << endl;
}