We start with a string $s$ consisting only of the digits $1$, $2$, or $3$. The length of $s$ is denoted by $|s|$. For each $i$ from $1$ to $|s|$, the $i$-th character of $s$ is denoted by $s_i$.

There is one cursor. The cursor's location $\ell$ is denoted by an integer in $\{0, \ldots, |s|\}$, with the following meaning:

• If $\ell = 0$, then the cursor is located before the first character of $s$.
• If $\ell = |s|$, then the cursor is located right after the last character of $s$.
• If $0 < \ell < |s|$, then the cursor is located between $s_\ell$ and $s_{\ell+1}$.

We denote by $s_\text{left}$ the string to the left of the cursor and $s_\text{right}$ the string to the right of the cursor.

We also have a string $c$, which we call our clipboard, which starts out as empty. There are three types of actions:

• The Move action. Move the cursor one step to the right. This increments $\ell$ once.
• The Cut action. Set $c \leftarrow s_\text{right}$, then set $s \leftarrow s_\text{left}$.
• The Paste action. Append the value of $c$ to the end of the string $s$. Note that this doesn't modify $c$.

The cursor initially starts at $\ell = 0$. Then, we perform the following procedure:

1. Perform the Move action once.
2. Perform the Cut action once.
3. Perform the Paste action $s_\ell$ times.
4. If $\ell = x$, stop. Otherwise, return to step 1.

You're given the initial string $s$ and the integer $x$. What is the length of $s$ when the procedure stops? Since this value may be very large, only find it modulo $10^9 + 7$.

It is guaranteed that $\ell \le |s|$ at any time.

The first line of input contains a single integer $t$ ($1 \le t \le 1000$) denoting the number of test cases. The next lines contain descriptions of the test cases.

The first line of each test case contains a single integer $x$ ($1 \le x \le 10^6$). The second line of each test case consists of the initial string $s$ ($1 \le |s| \le 500$). It is guaranteed, that $s$ consists of the characters "1", "2", "3".

It is guaranteed that the sum of $x$ in a single file is at most $10^6$. It is guaranteed that in each test case before the procedure will stop it will be true that $\ell \le |s|$ at any time.

For each test case, output a single line containing a single integer denoting the answer for that test case modulo $10^9 + 7$.