Problem: All bus tickets in Berland have their numbers. A number consists of n digits (n is even). Only k decimal digits d_1, d_2, ..., d_k can be used to form ticket numbers. If 0 is among these digits, then numbers may have leading zeroes. For example, if n = 4 and only digits 0 and 4 can be used, then 0000, 4004, 4440 are valid ticket numbers, and 0002, 00, 44443 are not.

A ticket is lucky if the sum of first n / 2 digits is equal to the sum of remaining n / 2 digits. 

Calculate the number of different lucky tickets in Berland. Since the answer may be big, print it modulo 998244353.

Input

The first line contains two integers n and k (2 ≤ n ≤ 2 ⋅ 10^5, 1 ≤ k ≤ 10) — the number of digits in each ticket number, and the number of different decimal digits that may be used. n is even.

The second line contains a sequence of pairwise distinct integers d_1, d_2, ..., d_k (0 ≤ d_i ≤ 9) — the digits that may be used in ticket numbers. The digits are given in arbitrary order.

Output

Print the number of lucky ticket numbers, taken modulo 998244353.

Examples

Input

4 2
1 8


Output

6


Input

20 1
6


Output

1


Input

10 5
6 1 4 0 3


Output

569725


Input

1000 7
5 4 0 1 8 3 2


Output

460571165

Note

In the first example there are 6 lucky ticket numbers: 1111, 1818, 1881, 8118, 8181 and 8888.

There is only one ticket number in the second example, it consists of 20 digits 6. This ticket number is lucky, so the answer is 1.

Solution (in JAVA):

Solution:
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.InputMismatchException;
import java.io.IOException;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
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);
        TaskG solver = new TaskG();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskG {
        static double[] cs = new double[1 << 21];
        static double[] sn = new double[1 << 21];
        static double[] csi = new double[1 << 21];
        static double[] sni = new double[1 << 21];

        static {
            for (int len = 1; len <= cs.length; len <<= 1) {
                for (int i = len / 2; i < len; i++) {
                    cs[i] = Math.cos(2 * Math.PI * (i - len / 2) / len);
                    sn[i] = Math.sin(2 * Math.PI * (i - len / 2) / len);
                    csi[i] = Math.cos(-2 * Math.PI * (i - len / 2) / len);
                    sni[i] = Math.sin(-2 * Math.PI * (i - len / 2) / len);
                }
            }
        }

        public void solve(int testNumber, InputReader in, PrintWriter out) {
            int mod = 998244353;
            int n = in.nextInt();
            int k = in.nextInt();
            int[] v = new int[10];
            for (int i = 0; i < k; i++) {
                int x = in.nextInt();
                v[x] = 1;
            }
            int[] ans = {1};
            int p = n / 2;
            while (true) {
                if (p % 2 != 0) {
                    ans = multiplyMod(ans, v, mod);
                }
                p /= 2;
                if (p == 0) break;
                v = multiplyMod(v, v, mod);
            }
            int res = 0;
            for (int x : ans) {
                res = (int) ((res + (long) x * x) % mod);
            }
            out.println(res);
        }

        static int[] multiplyMod(int[] a, int[] b, int mod) {
            int need = a.length + b.length - 1;
            int n = Math.max(2, Integer.highestOneBit(need - 1) << 1);

            double[] aReal = new double[n];
            double[] aImaginary = new double[n];
            for (int i = 0; i < a.length; i++) {
                int x = (a[i] % mod + mod) % mod;
                aReal[i] = x & ((1 << 15) - 1);
                aImaginary[i] = x >> 15;
            }
            fft(aReal, aImaginary, false);

            double[] bReal = new double[n];
            double[] bImaginary = new double[n];
            for (int i = 0; i < b.length; i++) {
                int x = (b[i] % mod + mod) % mod;
                bReal[i] = x & ((1 << 15) - 1);
                bImaginary[i] = x >> 15;
            }
            fft(bReal, bImaginary, false);

            double[] faReal = new double[n];
            double[] faImaginary = new double[n];
            double[] fbReal = new double[n];
            double[] fbImaginary = new double[n];

            for (int i = 0; i < n; i++) {
                int j = (n - i) & (n - 1);

                double a1r = (aReal[i] + aReal[j]) / 2;
                double a1i = (aImaginary[i] - aImaginary[j]) / 2;
                double a2r = (aImaginary[i] + aImaginary[j]) / 2;
                double a2i = (aReal[j] - aReal[i]) / 2;

                double b1r = (bReal[i] + bReal[j]) / 2;
                double b1i = (bImaginary[i] - bImaginary[j]) / 2;
                double b2r = (bImaginary[i] + bImaginary[j]) / 2;
                double b2i = (bReal[j] - bReal[i]) / 2;

                faReal[i] = a1r * b1r - a1i * b1i - a2r * b2i - a2i * b2r;
                faImaginary[i] = a1r * b1i + a1i * b1r + a2r * b2r - a2i * b2i;

                fbReal[i] = a1r * b2r - a1i * b2i + a2r * b1r - a2i * b1i;
                fbImaginary[i] = a1r * b2i + a1i * b2r + a2r * b1i + a2i * b1r;
            }

            fft(faReal, faImaginary, true);
            fft(fbReal, fbImaginary, true);
            int[] res = new int[need];
            for (int i = 0; i < need; i++) {
                long aa = (long) (faReal[i] + 0.5);
                long bb = (long) (fbReal[i] + 0.5);
                long cc = (long) (faImaginary[i] + 0.5);
                res[i] = (int) ((aa + ((bb % mod) << 15) + ((cc % mod) << 30)) % mod);
            }
            return res;
        }

        static void fft(double[] a, double[] b, boolean inverse) {
            int n = a.length;
            int shift = 32 - Integer.numberOfTrailingZeros(n);
            for (int i = 1; i < n; i++) {
                int j = Integer.reverse(i << shift);
                if (i < j) {
                    double temp = a[i];
                    a[i] = a[j];
                    a[j] = temp;
                    temp = b[i];
                    b[i] = b[j];
                    b[j] = temp;
                }
            }
            for (int len = 2; len <= n; len <<= 1) {
                int halfLen = len >> 1;
                for (int i = 0; i < n; i += len) {
                    int w = cs.length / len;
                    for (int j = 0, k = 0; j < halfLen; j++, k += w) {
                        double wA = inverse ? csi[halfLen + j] : cs[halfLen + j];
                        double wB = inverse ? sni[halfLen + j] : sn[halfLen + j];
                        double uA = a[i + j];
                        double uB = b[i + j];
                        double vA = a[i + j + halfLen] * wA - b[i + j + halfLen] * wB;
                        double vB = a[i + j + halfLen] * wB + b[i + j + halfLen] * wA;
                        a[i + j] = uA + vA;
                        b[i + j] = uB + vB;
                        a[i + j + halfLen] = uA - vA;
                        b[i + j + halfLen] = uB - vB;
                    }
                }
            }
            if (inverse) {
                for (int i = 0; i < n; i++) {
                    a[i] /= n;
                    b[i] /= n;
                }
            }
        }

    }

    static class InputReader {
        final InputStream is;
        final byte[] buf = new byte[1024];
        int pos;
        int size;

        public InputReader(InputStream is) {
            this.is = is;
        }

        public int nextInt() {
            int c = read();
            while (isWhitespace(c))
                c = read();
            int sign = 1;
            if (c == '-') {
                sign = -1;
                c = read();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res = res * 10 + c - '0';
                c = read();
            } while (!isWhitespace(c));
            return res * sign;
        }

        int read() {
            if (size == -1)
                throw new InputMismatchException();
            if (pos >= size) {
                pos = 0;
                try {
                    size = is.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (size <= 0)
                    return -1;
            }
            return buf[pos++] & 255;
        }

        static boolean isWhitespace(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

    }
}