p03228 Tenka1 Programmer Beginner Contest - Exchange
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.

Examples

Input

5 4 2


Output

5 3


Input

3 3 3


Output

1 3


Input

314159265 358979323 84


Output

448759046 224379523
```python
A, B, K = map(int,input().split())
for i in range(K):
    if i % 2 == 0:
        A -= (A % 2 == 1)
        A, B = A//2, B+A//2
    else:
        B -= (B % 2 == 1)
        A, B = A + B//2, B//2

print(A, B)
```