Recently, Peter saw the equation $x_{0}+2x_{1}+4x_{2}+...+2^{m}x_{m}=n$. He wants to find a solution $(x_0,x_1,x_2,...,x_m)$ in such a manner that $\displaystyle\sum_{i=0}^{m} x_i$ is minimum and every $x_i$ ($0 \le i \le m$) is non-negative.
Input
There are multiple test cases. The first line of input contains an integer $T$ $(1 \le T \le 10^5)$, indicating the number of test cases. For each test case:
The first contains two integers $n$ and $m$ $(0 \le n,m \le 10^9)$.
Output
For each test case, output the minimum value of $\displaystyle\sum_{i=0}^{m} x_i$.
