The Riddle

Eleonora's grandmother Sercha loves posing math riddles to her grandchildren. On the family's last trip she gave this one:

"Suppose a shop sells items priced from $1$ to $K$. I have $N$ coins whose denominations, in order, are $A_1, A_2, \ldots, A_N$. I am old and want to carry as few coins as possible. If I pick the coins up one by one starting from $A_1$, how many coins from the front must I take so that, using subsets of the coins I have taken, I can pay every price from $1$ to $K$ exactly?"

Eleonora answered within seconds and thought, "Basic algorithms like this are easy now!"

Help Eleonora. Taking the coins from the front in the given order, find the smallest number of coins that must be taken so that every amount from $1$ to $K$ can be formed as a subset sum of the taken coins. If this is impossible even after taking all $N$ coins, output $-1$.

The first line contains the number of test cases $T$.

For each test case, the first line contains two integers $N$ and $K$ ($N \le 100000$, $K \le 1000000$). The second line contains the $N$ coin denominations $A_1, A_2, \ldots, A_N$ in order, separated by spaces ($A_i \le 100000$).

For each test case, print on its own line the minimum number of coins that must be taken from the front so that every price from $1$ to $K$ can be paid as a subset sum of the taken coins. If it is impossible even after taking all $N$ coins, print $-1$.