Ecrade has an integer $$$x$$$. There are two kinds of operations.

Replace $$$x$$$ with $$$\left\lfloor \dfrac{x}{2}\right\rfloor$$$, where $$$\left\lfloor \dfrac{x}{2}\right\rfloor$$$ is the greatest integer $$$\le \dfrac{x}{2}$$$.
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!

Input

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 $$$m$$$ ($$$0 \le x, n, m \le 10^9$$$).

Output

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

Note

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 $$$2$$$.

Floor or Ceil

Examples