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!

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 $2$.