You are an expert competitive programmer. You will be given a problem statement, test case constraints and example test inputs and outputs. Please reason step by step about the solution (that must respect memory and time limits), then provide a complete implementation in python3.

Your solution must read input from standard input (cin), write output to standard output (cout).
Do not include any debug prints or additional output.

Put your final solution within a single code block:
```python
<your code here>
```

Execution time limit: 3.0 seconds
Memory limit: 256.0 MB

# Problem
Lunar New Year is approaching, and Bob received a gift from his friend recently — a recursive sequence! He loves this sequence very much and wants to play with it.

Let $$$f_1, f_2, \ldots, f_i, \ldots$$$ be an infinite sequence of positive integers. Bob knows that for $$$i > k$$$, $$$f_i$$$ can be obtained by the following recursive equation:

$$$$$$f_i = \left(f_{i - 1} ^ {b_1} \cdot f_{i - 2} ^ {b_2} \cdot \cdots \cdot f_{i - k} ^ {b_k}\right) \bmod p,$$$$$$

which in short is

$$$$$$f_i = \left(\prod_{j = 1}^{k} f_{i - j}^{b_j}\right) \bmod p,$$$$$$

where $$$p = 998\,244\,353$$$ (a widely-used prime), $$$b_1, b_2, \ldots, b_k$$$ are known integer constants, and $$$x \bmod y$$$ denotes the remainder of $$$x$$$ divided by $$$y$$$.

Bob lost the values of $$$f_1, f_2, \ldots, f_k$$$, which is extremely troublesome – these are the basis of the sequence! Luckily, Bob remembers the first $$$k - 1$$$ elements of the sequence: $$$f_1 = f_2 = \ldots = f_{k - 1} = 1$$$ and the $$$n$$$-th element: $$$f_n = m$$$. Please find any possible value of $$$f_k$$$. If no solution exists, just tell Bob that it is impossible to recover his favorite sequence, regardless of Bob's sadness.

## Input Format
The first line contains a positive integer $$$k$$$ ($$$1 \leq k \leq 100$$$), denoting the length of the sequence $$$b_1, b_2, \ldots, b_k$$$.

The second line contains $$$k$$$ positive integers $$$b_1, b_2, \ldots, b_k$$$ ($$$1 \leq b_i < p$$$).

The third line contains two positive integers $$$n$$$ and $$$m$$$ ($$$k < n \leq 10^9$$$, $$$1 \leq m < p$$$), which implies $$$f_n = m$$$.

## Output Format
Output a possible value of $$$f_k$$$, where $$$f_k$$$ is a positive integer satisfying $$$1 \leq f_k < p$$$. If there are multiple answers, print any of them. If no such $$$f_k$$$ makes $$$f_n = m$$$, output $$$-1$$$ instead.

It is easy to show that if there are some possible values of $$$f_k$$$, there must be at least one satisfying $$$1 \leq f_k < p$$$.

## Examples
```input
3
2 3 5
4 16
```
```output
4
```
-----
```input
5
4 7 1 5 6
7 14187219
```
```output
6
```
-----
```input
8
2 3 5 6 1 7 9 10
23333 1
```
```output
1
```
-----
```input
1
2
88888 66666
```
```output
-1
```
-----
```input
3
998244352 998244352 998244352
4 2
```
```output
-1
```
-----
```input
10
283 463 213 777 346 201 463 283 102 999
2333333 6263423
```
```output
382480067
```

## Note
In the first sample, we have $$$f_4 = f_3^2 \cdot f_2^3 \cdot f_1^5$$$. Therefore, applying $$$f_3 = 4$$$, we have $$$f_4 = 16$$$. Note that there can be multiple answers.

In the third sample, applying $$$f_7 = 1$$$ makes $$$f_{23333} = 1$$$.

In the fourth sample, no such $$$f_1$$$ makes $$$f_{88888} = 66666$$$. Therefore, we output $$$-1$$$ instead.

Now solve the problem and return the code.