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 javax.swing.Painter;

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


public class Main {
	
	static int mod = 998244353;
	static int g = 3;
	
	static long qpow(long a, long n) {
		long x = 1;
		a %= mod;
		while(n > 0) {
			if((n & 1) == 1) x = x * a % mod;
			a = a * a % mod; n >>= 1;
		}
		return x;
	}
	
	static void rader(long[] y, int len) {
		for(int i = 1, j = len / 2; i < len - 1; i++) {
			if(i < j) { long tmp = y[i]; y[i] = y[j]; y[j] = tmp; }
			int k = len / 2;
			while(j >= k) { j -= k; k /= 2; }
			if(j < k) j += k;
		}
	}
	
	static void NTT(long[] y, int len, int on) {
		rader(y, len);
		for(int h = 2; h <= len; h <<= 1) {
			long wn = qpow(g, (mod-1)/h);
			if(on == -1) wn = qpow(wn, mod-2);
			for(int j = 0; j < len; j += h) {
				long w = 1;
				for(int k = j; k < j + h / 2; k++) {
					long u = y[k];
					long t = w * y[k + h / 2] % mod;
					y[k] = (u + t) % mod;
					y[k+h/2] = (u - t + mod) % mod;
					w = w * wn % mod;
				}
			}
		}
		if(on == -1) {
			long t = qpow(len, mod - 2);
			for(int i = 0; i < len; i++)
				y[i] = y[i] * t % mod;
		}
	}
	
	public static void main(String[] args) throws IOException {
		FastScanner in = new FastScanner(new InputStreamReader(System.in));
		PrintWriter out = new PrintWriter(new OutputStreamWriter(System.out));
		
		int n = in.nextInt(), m = in.nextInt();
		int len = 1, nn = n / 2;
		while(len < (9 * nn + 1)) len <<= 1;
		long[] a = new long[len];
		long[] b = new long[len];
		
		a[0] = 1;
		for(int i = 0; i < m; i++) {
			int x = in.nextInt();
			b[x] = 1;
		}
		
		NTT(a, len, 1);
		NTT(b, len, 1);
		
		for(int i = 0; i < len; i++) {
			if(a[i] != 0 && b[i] != 0) {
				a[i] = a[i] * qpow(b[i], nn) % mod;
			} else a[i] = 0;
		}
		
		NTT(a, len, -1);
		
		long ans = 0;
		for(int i = 0; i < len; i++)
			ans = (ans + a[i] * a[i]) % mod;
		
		out.println((ans + mod) % mod);
		
		out.close();
    }
	
	static class FastScanner {
		private StringTokenizer ST;
		private BufferedReader BR;
		private PrintWriter PW;

		public FastScanner(InputStreamReader stream) {
			BR = new BufferedReader(stream);
		}

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

		public int nextInt() {
			return Integer.parseInt(next());
		}
		
		public long nextLong() {
	        return Long.parseLong(next());
	    }

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

	}
}