Cut and Paste
Description
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:
- Perform the Move action once.
- Perform the Cut action once.
- Perform the Paste action $s_\ell$ times.
- 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 $10^9 + 7$.
Input
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.
Output
For each test case, output a single line containing a single integer denoting the answer for that test case modulo $10^9 + 7$.
Samples
4
5
231
7
2323
6
333
24
133321333
25
1438
1101
686531475
Note
Let's illustrate what happens with the first test case. Initially, we have $s = $ 231. Initially, $\ell = 0$ and $c = \varepsilon$ (the empty string). The following things happen if we follow the procedure above:
- Step 1, Move once: we get $\ell = 1$.
- Step 2, Cut once: we get $s = $ 2 and $c = $ 31.
- Step 3, Paste $s_\ell = $ 2 times: we get $s = $ 23131.
- Step 4: $\ell = 1 \not= x = 5$, so we return to step 1.
- Step 1, Move once: we get $\ell = 2$.
- Step 2, Cut once: we get $s = $ 23 and $c = $ 131.
- Step 3, Paste $s_\ell = $ 3 times: we get $s = $ 23131131131.
- Step 4: $\ell = 2 \not= x = 5$, so we return to step 1.
- Step 1, Move once: we get $\ell = 3$.
- Step 2, Cut once: we get $s = $ 231 and $c = $ 31131131.
- Step 3, Paste $s_\ell = $ 1 time: we get $s = $ 23131131131.
- Step 4: $\ell = 3 \not= x = 5$, so we return to step 1.
- Step 1, Move once: we get $\ell = 4$.
- Step 2, Cut once: we get $s = $ 2313 and $c = $ 1131131.
- Step 3, Paste $s_\ell = $ 3 times: we get $s = $ 2313113113111311311131131.
- Step 4: $\ell = 4 \not= x = 5$, so we return to step 1.
- Step 1, Move once: we get $\ell = 5$.
- Step 2, Cut once: we get $s = $ 23131 and $c = $ 13113111311311131131.
- Step 3, Paste $s_\ell = $ 1 times: we get $s = $ 2313113113111311311131131.
- Step 4: $\ell = 5 = x$, so we stop.
At the end of the procedure, $s$ has length $25$.