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.util.*;
import java.io.*;
import java.lang.reflect.Array;
import java.math.BigInteger;

public class FFT {
	FastScanner in;
	PrintWriter out;
	boolean systemIO = true;

	public class Vector {
		int sz = 1 << 20;
		long[] v;
		
		public Vector(long[] a) {
			v = new long[sz];
			for (int i = 0; i < a.length; i++) {
				v[i] = a[i];
			}
		}
		
		public long[] FFT() {
			return DFT(0, 1, true);
		}
		
		public long[] FFT1() {
			long[] x = DFT(0, 1, false);
			for (int i = 0; i < x.length; i++) {
				x[i] = x[i] * szinv % mod;
			}
			return x;
		}
		
		public long[] DFT(int first, int pow, boolean straight) {
			if (pow == sz) {
				long[] ans = {v[first]};
				return ans;
			}
			long[] zero = DFT(first, 2 * pow, straight);
			long[] one = DFT(first + pow, 2 * pow, straight);
			int n = zero.length;
			long[] ans = new long[2 * n];
			for (int i = 0; i < n; i++) {
				ans[i] = (zero[i] + (straight ? warr[i * pow] : winvarr[i * pow]) * one[i]) % mod;
			}
			for (int i = 0; i < n; i++) {
				ans[n + i] = (((zero[i] - (straight ? warr[i * pow] : winvarr[i * pow]) * one[i]) % mod) + mod) % mod;
			}
			return ans;
		}
	}
	
	public long[] fft(long[] a) {
		long wth = 1;
		int sz = 1 << 20;
		long[] ans = new long[sz];
		for (int i = 0; i < ans.length; i++) {
			long x = 1;
			for (int j = 0; j < a.length; j++) {
				ans[i] += a[j] * x;
				ans[i] %= mod;
				x *= wth;
				x %= mod;
			}
			wth *= w;
			wth %= mod;
		}
		return ans;
	}
	
	public long[] pow(long[] ans, int p) {
		for (int i = 0; i < ans.length; i++) {
			ans[i] = pow(ans[i], p);
		}
		return ans;
	}
	
	public long pow(long x, int p) {
		if (p == 0) {
			return 1;
		}
		if (p % 2 == 1) {
			return pow(x, p - 1) * x % mod;
		}
		long y = pow(x, p / 2);
		return y * y % mod;
	}
	
	long mod = 998244353;
	long w = 646;
	long winv = (new BigInteger(w + "")).modInverse(new BigInteger(mod + "")).longValueExact();
	long[] warr = new long[1 << 20];
	long[] winvarr = new long[1 << 20];
	long szinv = (new BigInteger((1 << 20) + "")).modInverse(new BigInteger(mod + "")).longValueExact();

	public void solve() {
		int n = in.nextInt();
		int k = in.nextInt();
		long[] arr = new long[10];
		for (int i = 0; i < k; i++) {
			arr[in.nextInt()] = 1;
		}
		warr[0] = 1;
		winvarr[0] = 1;
		for (int i = 1; i < warr.length; i++) {
			warr[i] = warr[i - 1] * w % mod;
			winvarr[i] = winvarr[i - 1] * w % mod;
		}
		long[] x = fft(arr);
		x = pow(x, n / 2);
		Vector v = new Vector(x);
		x = v.FFT1();
		long ans = 0;
		for (int i = 0; i < x.length; i++) {
			ans += x[i] * x[i];
			ans %= mod;
		}
		out.println(ans);
	}

	public void run() {
		try {
			if (systemIO) {
				in = new FastScanner(System.in);
				out = new PrintWriter(System.out);
			} else {
				in = new FastScanner(new File("input.txt"));
				out = new PrintWriter(new File("output.txt"));
			}
			solve();

			out.close();
		} catch (IOException e) {
			e.printStackTrace();
		}
	}

	class FastScanner {
		BufferedReader br;
		StringTokenizer st;

		FastScanner(File f) {
			try {
				br = new BufferedReader(new FileReader(f));
			} catch (FileNotFoundException e) {
				e.printStackTrace();
			}
		}

		FastScanner(InputStream f) {
			br = new BufferedReader(new InputStreamReader(f));
		}

		String nextLine() {
			try {
				return br.readLine();
			} catch (IOException e) {
				return null;
			}
		}

		String next() {
			while (st == null || !st.hasMoreTokens()) {
				try {
					st = new StringTokenizer(br.readLine());
				} catch (IOException e) {
					e.printStackTrace();
				}
			}
			return st.nextToken();
		}

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

		long nextLong() {
			return Long.parseLong(next());
		}

		double nextDouble() {
			return Double.parseDouble(next());
		}

	}

	// AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
	public static void main(String[] arg) {
		new FFT().run();
	}
}