A13186 | Fill The Bag

You have a bag of size $n$ . Also you have $m$ boxes. The size of $i$ -th box is $a_i$ , where each $a_i$ is an integer non-negative power of two.

You can divide boxes into two parts of equal size. Your goal is to fill the bag completely.

For example, if $n = 10$ and $a = [1, 1, 32]$ then you have to divide the box of size $32$ into two parts of size $16$ , and then divide the box of size $16$ . So you can fill the bag with boxes of size $1$ , $1$ and $8$ .

Calculate the minimum number of divisions required to fill the bag of size $n$ .

The first line contains one integer $t$ ( $1 \le t \le 1000$ ) — the number of test cases.

The first line of each test case contains two integers $n$ and $m$ ( $1 \le n \le 10^{18}, 1 \le m \le 10^5$ ) — the size of bag and the number of boxes, respectively.

The second line of each test case contains $m$ integers $a_1, a_2, \dots , a_m$ ( $1 \le a_i \le 10^9$ ) — the sizes of boxes. It is guaranteed that each $a_i$ is a power of two.

It is also guaranteed that sum of all $m$ over all test cases does not exceed $10^5$ .

For each test case print one integer — the minimum number of divisions required to fill the bag of size $n$ (or $-1$ , if it is impossible).