Problem:
Score : 100 points

Problem Statement

We have N+M balls, each of which has an integer written on it.

It is known that:

The numbers written on N of the balls are even.

The numbers written on M of the balls are odd.

Find the number of ways to choose two of the N+M balls (disregarding order) so that the sum of the numbers written on them is even.

It can be shown that this count does not depend on the actual values written on the balls.

Constraints

0 \leq N,M \leq 100

2 \leq N+M

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N M

Output

Print the answer.

Sample Input 1

2 1

Sample Output 1

1

For example, let us assume that the numbers written on the three balls are 1,2,4.

If we choose the two balls with 1 and 2, the sum is odd;

If we choose the two balls with 1 and 4, the sum is odd;

If we choose the two balls with 2 and 4, the sum is even.

Thus, the answer is 1.

Sample Input 2

4 3

Sample Output 2

9

Sample Input 3

1 1

Sample Output 3

0

Sample Input 4

13 3

Sample Output 4

81

Sample Input 5

0 3

Sample Output 5

3

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Runtime Error)

import java.io.*;
import java.util.*;

import static java.lang.Math.*;

public class Main {
    static public class pair {
        int u;
        int idx;
        int val;

        public pair(int x, int i) {
            u = x;
            idx = i;
            val = -1;
        }
    }

    static public class trp implements Comparable<trp> {

        int idx;
        int val;

        public trp(int v, int i) {
            idx = i;
            val = v;
        }

        @Override
        public int compareTo(trp trp) {
            return idx - trp.idx;
        }
    }

    static int[] color;
    static ArrayList<pair>[] adj;
    static int[] Arr, Arry;
    static int inf = (int) 1e9, n, s, h, x, y;
    static boolean[][] matrix;
    static long[][] memo;
    static long mod = 998244353;

    public static long dp(int idx, int rem) {
        if (idx == n||rem<0)
            return rem == 0 ? 1 : 0;
        if(memo[idx][rem]!=-1)return memo[idx][rem];
        long end = rem == 0 ? 1 : 0;
        long take = dp(idx + 1, rem - Arr[idx]);
        long leave = dp(idx + 1, rem);
        return memo[idx][rem]=(end % mod + take % mod + leave % mod) % mod;
    }

    public static boolean isBadrome(String str) {
        for (int i = 0; i <= str.length() / 2; i++)
            if (str.charAt(i) != str.charAt(str.length() - 1 - i))
                return false;
        return true;


    }

    public static void main(String[] args) throws Exception {
//        Scanner sc = new Scanner("kitchen.in");
//        PrintWriter pw = new PrintWriter("kitchen.out");
        Scanner sc = new Scanner(System.in);
        PrintWriter pw = new PrintWriter(System.out);
        n = sc.nextInt();
        s = sc.nextInt();
        Arr = new int[n];
        for (int i = 0; i < n; i++)
            Arr[i] = sc.nextInt();
        long ans = 0;
        memo=new long[n][s+1];
        for(long []x:memo)Arrays.fill(x, -1);
        for (int i = 0; i < n; i++) {
            ans += dp(i, s);
            ans%=mod;
        }
        pw.println(ans);
        pw.close();
    }

    public static class Scanner {
        StringTokenizer st;
        BufferedReader br;

        public Scanner(InputStream s) {
            br = new BufferedReader(new InputStreamReader(s));
        }

        public Scanner(String s) throws FileNotFoundException {
            br = new BufferedReader(new FileReader(s));

        }

        public String next() throws IOException {
            while (st == null || !st.hasMoreTokens())
                st = new StringTokenizer(br.readLine());
            return st.nextToken();
        }

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

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

        public String nextLine() throws IOException {
            return br.readLine();
        }

        public double nextDouble() throws IOException {
            String x = next();
            StringBuilder sb = new StringBuilder("0");
            double res = 0, f = 1;
            boolean dec = false, neg = false;
            int start = 0;
            if (x.charAt(0) == '-') {
                neg = true;
                start++;
            }
            for (int i = start; i < x.length(); i++)
                if (x.charAt(i) == '.') {
                    res = Long.parseLong(sb.toString());
                    sb = new StringBuilder("0");
                    dec = true;
                } else {
                    sb.append(x.charAt(i));
                    if (dec)
                        f *= 10;
                }
            res += Long.parseLong(sb.toString()) / f;
            return res * (neg ? -1 : 1);
        }

        public boolean ready() throws IOException, IOException {
            return br.ready();
        }

    }
}