Description

Input

The first line contains a single integer $t$ ($1 \leq t \leq 10^4$) — the number of test cases.

The first line of each test case contains two integers $n$ and $s$ ($1 \leq n, s \leq 2 \cdot 10^5$) — the length of the array and the needed sum of elements.

The second line of each test case contains $n$ integers $a_i$ ($0 \leq a_i \leq 1$) — the elements of the array.

It is guaranteed that the sum of $n$ over all test cases doesn't exceed $2 \cdot 10^5$.

Output

For each test case, output a single integer — the minimum amount of operations required to have the total sum of the array equal to $s$, or -1 if obtaining an array with sum $s$ isn't possible.

7
3 1
1 0 0
3 1
1 1 0
9 3
0 1 0 1 1 1 0 0 1
6 4
1 1 1 1 1 1
5 1
0 0 1 1 0
16 2
1 1 0 0 1 0 0 1 1 0 0 0 0 0 1 1
6 3
1 0 1 0 0 0
 
 
 
 
 
 
 
 

0
1
3
2
2
7
-1

Note

In the first test case, the sum of the whole array is $1$ from the beginning, so we don't have to make any operations.

In the second test case, the sum of the array is $2$ and we want it to be equal to $1$, so we should remove the first element. The array turns into $[1, 0]$, which has a sum equal to $1$.

In the third test case, the sum of the array is $5$ and we need it to be $3$. We can obtain such a sum by removing the first two elements and the last element, doing a total of three operations. The array turns into $[0, 1, 1, 1, 0, 0]$, which has a sum equal to $3$.