Moving

You want to move from position $1$ to position $N$ on a number line. At position $i$, you may move right by any integer from $1$ through $A_i$.

Find the minimum number of moves required to reach position $N$ exactly. Print t{-1} if it is unreachable.

The input is given in the following format:

$T$ case$_1$ case$_2$ $\vdots$ case$_T$

Each test case is given in the following format:

$N$ $A_1\ A_2\ \cdots\ A_N$

For each test case, print the minimum number of moves on one line. Print -1 if position $N$ is unreachable.

• $1 \leq T \leq 100$.
• $1 \leq N \leq 200\,000$.
• $0 \leq A_i \leq N$ ($1 \leq i \leq N$).
• The sum of $N$ over all test cases does not exceed $200\,000$.