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, …, f_i, … be an infinite sequence of positive integers. Bob knows that for i > k, f_i can be obtained by the following recursive equation:

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

which in short is

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

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

Bob lost the values of f_1, f_2, …, 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 = … = 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

The first line contains a positive integer k (1 ≤ k ≤ 100), denoting the length of the sequence b_1, b_2, …, b_k.

The second line contains k positive integers b_1, b_2, …, b_k (1 ≤ b_i < p).

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

Output

Output a possible value of f_k, where f_k is a positive integer satisfying 1 ≤ 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 ≤ 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 ⋅ f_2^3 ⋅ 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.

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.*;

public class Main {

    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskF solver = new TaskF(in, out);
        solver.solve();
        out.close();
    }

    static class TaskF {
        static private final int MOD = 998244353;

        private InputReader in;
        private PrintWriter out;

        TaskF(InputReader in, PrintWriter out) {
            this.in = in;
            this.out = out;
        }

        private void solve() {
            int k = in.nextInt();
            int[] coeffs = new int[k];
            for (int i = 0; i < k; ++i) {
                coeffs[i] = in.nextInt();
            }

            int n = in.nextInt();
            int value = in.nextInt();

            Matrix trans = new Matrix(k);
            for (int i = 0; i < k - 1; ++i) {
                trans.setValueOf(i + 1, i, 1);
            }
            for (int i = 0; i < k; ++i) {
                trans.setValueOf(i, k - 1, coeffs[k - 1 - i]);
            }

            int power = Matrix.binPow(trans, n - k).getValueOf(k - 1, k - 1);
            int answer = solve(power, value);
            out.println(answer);
        }

        static private int add(int x, int y, int MOD) {
            return (x + y >= MOD ? x + y - MOD : x + y);
        }

        static private int mul(int x, int y, int MOD) {
            return (int)((long)x * y % MOD);
        }

        private int binPow(int base, int exp, int MOD) {
            int result = 1;
            for (; exp > 0; exp /= 2) {
                if (exp % 2 == 1) {
                    result = mul(result, base, MOD);
                }
                base = mul(base, base, MOD);
            }
            return result;
        }

        private int babyStep(int base, int result, int MOD) {
            int lim = (int)Math.sqrt(MOD) + 1;
            Map<Integer, Integer> values = new HashMap<>();
            for (int i = 1; i <= lim; ++i) {
                int current = binPow(base, mul(i, lim, MOD - 1), MOD);
                values.put(current, i);
            }
            for (int i = 0; i <= lim; ++i) {
                int current = mul(result, binPow(base, i, MOD), MOD);
                if (values.containsKey(current)) {
                    int answer = values.get(current) * lim - i;
                    if (answer < MOD) {
                        return answer;
                    }
                }
            }
            return -1;
        }

        private int solve(int power, int result) {
            // x^power = result (modulo MOD)

            if (result == 1) {
                return 1;
            }
            if (power == 0) {
                return -1;
            }
            int primitiveRoot = 3;
            int logarithmBase = binPow(primitiveRoot, power, MOD);
            int primitivePower = babyStep(logarithmBase, result, MOD);
            if (primitivePower == -1) {
                return -1;
            }
            int answer = binPow(primitiveRoot, primitivePower, MOD);
            assert(binPow(answer, power, MOD) == result);
            return answer;
        }

        static class Matrix {
            private int size;
            int[][] mtrx;

            private Matrix(int n) {
                size = n;
                mtrx = new int[size][size];
                for (int i = 0; i < n; ++i) {
                    for (int j = 0; j < n; ++j) {
                        mtrx[i][j] = 0;
                    }
                }
            }

            private int getSize() {
                return size;
            }

            private int getValueOf(int i, int j) {
                return mtrx[i][j];
            }

            private void setValueOf(int i, int j, int value) {
                mtrx[i][j] = value;
            }

            private void incValueOf(int i, int j, int value) {
                mtrx[i][j] = add(mtrx[i][j], value, MOD - 1);
            }

            static private Matrix IdentityMatrix(int n) {
                Matrix base = new Matrix(n);
                for (int i = 0; i < n; ++i) {
                    base.setValueOf(i, i, 1);
                }
                return base;
            }

            static private Matrix multiply(Matrix lhs, Matrix rhs) {
                int n = lhs.getSize();
                Matrix result = new Matrix(n);
                for (int i = 0; i < n; ++i) {
                    for (int j = 0; j < n; ++j) {
                        for (int k = 0; k < n; ++k) {
                            int temp = mul(lhs.getValueOf(i, k), rhs.getValueOf(k, j), MOD - 1);
                            result.incValueOf(i, j, temp);
                        }
                    }
                }
                return result;
            }

            static private Matrix binPow(Matrix matrix, int exp) {
                Matrix result = IdentityMatrix(matrix.getSize());
                for (; exp > 0; exp /= 2) {
                    if (exp % 2 == 1) {
                        result = multiply(result, matrix);
                    }
                    matrix = multiply(matrix, matrix);
                }
                return result;
            }
        }
    }

    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

    }

}