Description
A program a day keep girls away.
~by anonymous programmer
You are a programmer, you need to write code day and night.
In order to keep you in a sharp mind, you drink a lot of coffee.
Given n cups of coffee, the ith cup of coffee has the effect that make
you write ai lines of code.
Each cup of coffee can only be drunk for once.
You can drink coffee in arbitary order!!!!
You need to write more than m lines of code.
In a day when you drink a cup of coffee,
the second cup of coffee will loss it's effect by 1
and the third cup of coffee will loss it's effect by 2
..... and so on
You need to find out what's the minimum number of days
that you can write more than m lines of code.
Example:
Given n = 5 cups of coffee, you need to finish m=16 lines of code.
The effect of coffee = a1 = 5, a2 = 5, a3 = 5, a4 = 5, a5 = 5
If you drink a1~a4 at the first day, you finish 5 + (5-1) + (5-2) + (5-3) = 14 lines of code.
If you drink a5 at the second day, you finish 5 lines of code.
14+5 > 16 therefore you can finish your code by 2 days,
and it's the minimum number of days that you can achieve.
Input
First line contains one integer t(1 <= t <= 10) which means the number of testcases.
Each testcases contains two lines.
First line contains two integer n(1 <= n <= 2*10^5), m(1 <= m <= 10^9)
Second line contains n numbers ai(1 <= ai <= 10^9)
Output
For each testcase print only one number which means the minimum number of days
that you can write more than m lines of code.
If you can't finish your code in any way, print -1.
Remember to print \n at the end of output.