Force Perturbation
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Description
The impacts of the creation of "palindromio" by Javier and his friends have reached Esomer (who is capable of measuring when the forces of order become unbalanced in the universe).
Esomer is able to sense that the Force has become unbalanced in an integer $x$. Being the busy sage that he is, he doesn't have time to restore it and will need to make use of his $n$ students to restore the Force. Each student has a power of $a_i$, and choosing them will reduce the difference of $x$ to $x - a_i$. Every day that passes, all his students increase their power by $1$.
Help him remedy this perturbation as soon as possible, that is, print the minimum number of days in which the difference $x$ can be reduced to exactly $0$ using his students.
Once Esomer has used one of his students, due to their fatigue, he will not be able to use them again.
The first line contains an integer $t$, ($1 \le t \le 10$), the number of cases to solve.
Each of the cases will consist of two integers $n$, the number of students he has ($1 \le n \le 200$), and $x$, the imbalance that has occurred in the force ($1 \le x \le 200$).
$n$ integers will follow, the sequence $a_1, a_2,..., a_n$, where $a_i$ represents the strength of the i-th student ($1 \le a_i \le x$).
It is guaranteed that the sums of $n$ and $x$ over all cases will not exceed $200$.
For each case, you should print a single integer, the minimum number of days that must pass for Esomer to reduce $x$ to $0$.
Input
The first line contains an integer $t$, ($1 \le t \le 10$), the number of cases to solve.
Each of the cases will consist of two integers $n$, the number of students he has ($1 \le n \le 200$), and $x$, the imbalance that has occurred in the force ($1 \le x \le 200$).
$n$ integers will follow, the sequence $a_1, a_2,..., a_n$, where $a_i$ represents the strength of the i-th student ($1 \le a_i \le x$).
It is guaranteed that the sums of $n$ and $x$ over all cases will not exceed $200$.
Output
For each case, you should print a single integer, the minimum number of days that must pass for Esomer to reduce $x$ to $0$.
1
3 4
1 1 1
1
Note
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Problem idea: Javi
Problem preparation: Javi
Ocurrences: Advanced 3