CF2082B Floor or Ceil

Ecrade has an integer $ x $ . There are two kinds of operations. 1. Replace $ x $ with $ \left\lfloor \dfrac{x}{2}\right\rfloor $ , where $ \left\lfloor \dfrac{x}{2}\right\rfloor $ is the greatest integer $ \le \dfrac{x}{2} $ . 2. Replace $ x $ with $ \left\lceil \dfrac{x}{2}\right\rceil $ , where $ \left\lceil \dfrac{x}{2}\right\rceil $ is the smallest integer $ \ge \dfrac{x}{2} $ . Ecrade will perform exactly $ n $ first operations and $ m $ second operations in any order. He wants to know the minimum and the maximum possible value of $ x $ after $ n+m $ operations. However, it seems a little difficult, so please help him!

Each test contains multiple test cases. The first line contains the number of test cases $ t $ ( $ 1 \le t \le 10^4 $ ). The description of the test cases follows. The only line of each test case contains three integers $ x $ , $ n $ , and $ m $ ( $ 0 \le x, n, m \le 10^9 $ ).

For each test case, print two integers in one line, representing the minimum and the maximum possible value of $ x $ after $ n + m $ operations.

For simplicity, we call the first operation $ \text{OPER 1} $ and the second operation $ \text{OPER 2} $ . In the first test case: - If we perform $ 12 \xrightarrow{\text{OPER 2}} 6 \xrightarrow{\text{OPER 2}} 3 \xrightarrow{\text{OPER 1}} 1 $ , we can obtain the minimum possible value $ 1 $ . - If we perform $ 12 \xrightarrow{\text{OPER 2}} 6 \xrightarrow{\text{OPER 1}} 3 \xrightarrow{\text{OPER 2}} 2 $ , we can obtain the maximum possible value $ 2 $ .