Aaronson

Time Limit: 4000/2000 MS (Java/Others)

Memory Limit: 131072/131072 K (Java/Others)

Description

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 $\displaystyle\sum_{i=0}^{m} x_i$.

Sample Input

10 1 2 3 2 5 2 10 2 10 3 10 4 13 5 20 4 11 11 12 3

Sample Output

1 2 2 3 2 2 3 2 3 2

Hint

wange2014

Source

BestCoder Round #84

提交代码