DreamGrid has an integer sequence $a_1, a_2, \dots, a_n$ and he likes it very much. Unfortunately, h

DreamGrid has an integer sequence $a_1,a_2,\dots ,a_n$ and he likes it very much. Unfortunately, his naughty roommate BaoBao swapped two elements $a_i$ and $a_j$ ($1\le i<j\le n$) in the sequence when DreamGrid wasn’t at home. When DreamGrid comes back, he finds with dismay that his precious sequence has been changed into $a_1,a_2,\dots a_{i-1},a_j,a_{i+1},\dots ,a_{j-1},a_i,a_{j+1},\dots ,a_n$!

What’s worse is that DreamGrid cannot remember his precious sequence. What he only remembers are the two values $$x=\sum _{k=1}^{n}k{a}_k\text{and}y=\sum _{k=1}^{n}k{a}_k^2$$ Given the sequence after swapping and the two values DreamGrid remembers, please help DreamGrid count the number of possible element pairs $(a_i,a_j)$ BaoBao swaps.

Note that as DreamGrid is poor at memorizing numbers, the value of $x$ or $y$ might not match the sequence, and no possible element pair can be found in this situation.

Two element pairs $(a_i,a_j)$ ($1\le i<j\le n$) and $(a_p,a_q)$ ($1\le p<q\le n$) are considered different if $i\ne p$ or $j\ne q$.
Input

There are multiple test cases. The first line of the input contains an integer $T$, indicating the number of test cases. For each test case:

The first line contains three integers $n$, $x$ and $y$ ($2\le n\le 10^5,1\le x,y\le 10^{18}$), indicating the length of the sequence and the two values DreamGrid remembers.

The second line contains $n$ integers $b_1,b_2,\dots ,b_n$ ($1\le b_i\le 10^5$), indicating the sequence after swapping. It’s guaranteed that $\sum _{k=1}^{n}k{b}_k\le 10^{18}$ and $\sum _{k=1}^{n}k{b}_k^2\le 10^{18}$.

It’s guaranteed that the sum of $n$ of all test cases will not exceed $2\times 10^6$.
Output

For each test case output one line containing one integer, indicating the number of possible element pairs BaoBao swaps.
Sample Input

2
6 61 237
1 1 4 5 1 4
3 20190429 92409102
1 2 3

Sample Output

2
0

Hint

For the first sample test case, it’s possible that BaoBao swaps the 2nd and the 3rd element, or the 5th and the 6th element.