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.Arrays;
import java.io.FilterInputStream;
import java.io.BufferedInputStream;
import java.io.InputStream;

/**
 * @author khokharnikunj8
 */

public class Main {
    public static void main(String[] args) {
        new Thread(null, new Runnable() {
            public void run() {
                new Main().solve();
            }
        }, "1", 1 << 26).start();
    }

    void solve() {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        ScanReader in = new ScanReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        GLuckyTickets solver = new GLuckyTickets();
        solver.solve(1, in, out);
        out.close();
    }

    static class GLuckyTickets {
        static final long mask = (1L << 31) - 1;
        int mod = 998244353;
        int[] d;

        public static long[] convoluteSimply(long[] a, long[] b, int P, int g) {
            int m = Math.max(2, Integer.highestOneBit(Math.max(a.length, b.length) - 1) << 2);
            long[] fa = nttmb(a, m, false, P, g);
            long[] fb = a == b ? fa : nttmb(b, m, false, P, g);
            for (int i = 0; i < m; i++) {
                fa[i] = fa[i] * fb[i] % P;
            }
            return nttmb(fa, m, true, P, g);
        }

        private static long[] nttmb(long[] src, int n, boolean inverse, int P, int g) {
            long[] dst = Arrays.copyOf(src, n);

            int h = Integer.numberOfTrailingZeros(n);
            long K = Integer.highestOneBit(P) << 1;
            int H = Long.numberOfTrailingZeros(K) * 2;
            long M = K * K / P;

            int[] wws = new int[1 << h - 1];
            long dw = inverse ? pow(g, P - 1 - (P - 1) / n, P) : pow(g, (P - 1) / n, P);
            long w = (1L << 32) % P;
            for (int k = 0; k < 1 << h - 1; k++) {
                wws[k] = (int) w;
                w = modh(w * dw, M, H, P);
            }
            long J = invl(P, 1L << 32);
            for (int i = 0; i < h; i++) {
                for (int j = 0; j < 1 << i; j++) {
                    for (int k = 0, s = j << h - i, t = s | 1 << h - i - 1; k < 1 << h - i - 1; k++, s++, t++) {
                        long u = (dst[s] - dst[t] + 2 * P) * wws[k];
                        dst[s] += dst[t];
                        if (dst[s] >= 2 * P) dst[s] -= 2 * P;
//					long Q = (u&(1L<<32)-1)*J&(1L<<32)-1;
                        long Q = (u << 32) * J >>> 32;
                        dst[t] = (u >>> 32) - (Q * P >>> 32) + P;
                    }
                }
                if (i < h - 1) {
                    for (int k = 0; k < 1 << h - i - 2; k++) wws[k] = wws[k * 2];
                }
            }
            for (int i = 0; i < n; i++) {
                if (dst[i] >= P) dst[i] -= P;
            }
            for (int i = 0; i < n; i++) {
                int rev = Integer.reverse(i) >>> -h;
                if (i < rev) {
                    long d = dst[i];
                    dst[i] = dst[rev];
                    dst[rev] = d;
                }
            }

            if (inverse) {
                long in = invl(n, P);
                for (int i = 0; i < n; i++) dst[i] = modh(dst[i] * in, M, H, P);
            }

            return dst;
        }

        public static long modh(long a, long M, int h, int mod) {
            long r = a - ((M * (a & mask) >>> 31) + M * (a >>> 31) >>> h - 31) * mod;
            return r < mod ? r : r - mod;
        }

        private static long pow(long a, long n, long mod) {
            //		a %= mod;
            long ret = 1;
            int x = 63 - Long.numberOfLeadingZeros(n);
            for (; x >= 0; x--) {
                ret = ret * ret % mod;
                if (n << 63 - x < 0)
                    ret = ret * a % mod;
            }
            return ret;
        }

        private static long invl(long a, long mod) {
            long b = mod;
            long p = 1, q = 0;
            while (b > 0) {
                long c = a / b;
                long d;
                d = a;
                a = b;
                b = d % b;
                d = p;
                p = q;
                q = d - c * q;
            }
            return p < 0 ? p + mod : p;
        }

        public void solve(int testNumber, ScanReader in, PrintWriter out) {
            int n = in.scanInt();
            int k = in.scanInt();
            this.mod = 998244353;
            d = new int[k];
            for (int i = 0; i < k; i++) d[i] = in.scanInt();
            long ans = 0;
            long[] temp = new long[10];
            for (int i : d) temp[i]++;
            long[] dp = null;
            n /= 2;
            while (n > 0) {
                if ((n & 1) == 1) {
                    if (dp == null) dp = Arrays.copyOf(temp, temp.length);
                    else {
                        long[] dp1 = new long[temp.length];
                        for (int i = 0; i < dp.length; i++) dp1[i] = dp[i];
                        dp = convoluteSimply(dp1, temp, mod, 3);
                    }
                }
                n >>= 1;
                temp = convoluteSimply(temp, temp, mod, 3);
            }


            for (int i = 0; i < dp.length; i++) {
                ans = (ans + ((dp[i] * dp[i]) % mod)) % mod;
            }
            out.println(ans);
        }

    }

    static class ScanReader {
        private byte[] buf = new byte[4 * 1024];
        private int index;
        private BufferedInputStream in;
        private int total;

        public ScanReader(InputStream inputStream) {
            in = new BufferedInputStream(inputStream);
        }

        private int scan() {
            if (index >= total) {
                index = 0;
                try {
                    total = in.read(buf);
                } catch (Exception e) {
                    e.printStackTrace();
                }
                if (total <= 0) return -1;
            }
            return buf[index++];
        }

        public int scanInt() {
            int integer = 0;
            int n = scan();
            while (isWhiteSpace(n)) n = scan();
            int neg = 1;
            if (n == '-') {
                neg = -1;
                n = scan();
            }
            while (!isWhiteSpace(n)) {
                if (n >= '0' && n <= '9') {
                    integer *= 10;
                    integer += n - '0';
                    n = scan();
                }
            }
            return neg * integer;
        }

        private boolean isWhiteSpace(int n) {
            if (n == ' ' || n == '\n' || n == '\r' || n == '\t' || n == -1) return true;
            else return false;
        }

    }
}