Problem: zscoder has a deck of n+m custom-made cards, which consists of n cards labelled from 1 to n and m jokers. Since zscoder is lonely, he wants to play a game with himself using those cards. 

Initially, the deck is shuffled uniformly randomly and placed on the table. zscoder has a set S which is initially empty. 

Every second, zscoder draws the top card from the deck. 

  * If the card has a number x written on it, zscoder removes the card and adds x to the set S. 
  * If the card drawn is a joker, zscoder places all the cards back into the deck and reshuffles (uniformly randomly) the n+m cards to form a new deck (hence the new deck now contains all cards from 1 to n and the m jokers). Then, if S currently contains all the elements from 1 to n, the game ends. Shuffling the deck doesn't take time at all. 



What is the expected number of seconds before the game ends? We can show that the answer can be written in the form P/Q where P, Q are relatively prime integers and Q ≠ 0 mod 998244353. Output the value of (P ⋅ Q^{-1}) modulo 998244353.

Input

The only line of the input contains two integers n and m (1 ≤ n, m ≤ 2 ⋅ 10^{6}).

Output

Output a single integer, the value of (P ⋅ Q^{-1}) modulo 998244353.

Examples

Input


2 1


Output


5


Input


3 2


Output


332748127


Input


14 9


Output


969862773

Note

For the first sample, it can be proven that the expected time before the game ends is 5 seconds.

For the second sample, it can be proven that the expected time before the game ends is 28/3 seconds.

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.IOException;
import java.io.InputStreamReader;
import java.util.StringTokenizer;
import java.io.BufferedReader;
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);
        HZSShufflesCards solver = new HZSShufflesCards();
        solver.solve(1, in, out);
        out.close();
    }

    static class HZSShufflesCards {
        NumberTheory.Mod998 mod = new NumberTheory.Mod998();
        int n;
        int m;

        public void solve(int testNumber, InputReader in, PrintWriter out) {
            n = in.nextInt();
            m = in.nextInt();

            mod.fInv(n + m);

            long phaseSize = 1;
            long p = 1;
            for (int i = 0; p != 0; i++) {
                p = mod.mult(p, n - i, mod.smallInv(n + m - i));
                phaseSize = mod.add(phaseSize, p);
            }

            long answer = 0;
            for (int k = 1; k <= n; k++) {
                long sign = mod.paritySign(k + 1);
                long numPhases = mod.mult(m + k, mod.smallInv(k));
                long term = mod.mult(sign, mod.ncr(n, k), numPhases, phaseSize);
                answer = mod.add(answer, term);
            }

            out.println(answer);
        }

    }

    static class InputReader {
        public final BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

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

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

    }

    static class Util {
        public static void ASSERT(boolean assertion) {
            if (!assertion)
                throw new AssertionError();
        }

        private Util() {
        }

    }

    static class IntStack {
        int[] array;
        int size = 0;

        public IntStack() {
            this(8);
        }

        public IntStack(int capacity) {
            array = new int[capacity];
        }

        public void push(int item) {
            if (size >= array.length)
                array = resize(array);
            array[size++] = item;
        }

        public int size() {
            return size;
        }

        public int get(int i) {
            Util.ASSERT(i < size);
            return array[i];
        }

        private static int[] resize(int[] array) {
            int[] newArray = new int[array.length << 1];
            System.arraycopy(array, 0, newArray, 0, array.length);
            return newArray;
        }

        public String toString() {
            int[] trimmed = new int[size];
            System.arraycopy(array, 0, trimmed, 0, size);
            return Arrays.toString(trimmed);
        }

    }

    static class NumberTheory {
        private static void ASSERT(boolean assertion) {
            if (!assertion)
                throw new AssertionError();
        }

        public abstract static class Modulus<M extends NumberTheory.Modulus<M>> {
            final IntStack factorial = new IntStack();
            final IntStack invFactorial = new IntStack();

            public abstract long modulus();

            public Modulus() {
                super();
                factorial.push(1);
                invFactorial.push(1);
            }

            public long fact(int n) {
                while (factorial.size() <= n) {
                    factorial.push((int) mult(factorial.get(factorial.size() - 1), factorial.size()));
                }

                return factorial.get(n);
            }

            public long fInv(int n) {
                int lastKnown = invFactorial.size() - 1;

                if (lastKnown < n) {
                    long[] fInv = new long[n - lastKnown];
                    fInv[0] = inv(fact(n));
                    for (int i = 1; i < fInv.length; i++) {
                        fInv[i] = mult(fInv[i - 1], n - i + 1);
                    }
                    for (int i = fInv.length - 1; i >= 0; i--) {
                        invFactorial.push((int) fInv[i]);
                    }
                }

                return invFactorial.get(n);
            }

            public long paritySign(long k) {
                return (k & 1) == 0 ? 1 : modulus() - 1;
            }

            public long ncr(int n, int r) {
                ASSERT(n >= 0);
                if (r < 0 || n < r)
                    return 0;
                return mult(fact(n), mult(fInv(r), fInv(n - r)));
            }

            public long smallInv(int n) {
                return mult(fInv(n), fact(n - 1));
            }

            public long normalize(long x) {
                x %= modulus();
                if (x < 0)
                    x += modulus();
                return x;
            }

            public long add(long a, long b) {
                long v = a + b;
                return v < modulus() ? v : v - modulus();
            }

            public long mult(long... x) {
                long r = 1;
                for (long i : x)
                    r = mult(r, i);
                return r;
            }

            public long mult(long a, long b) {
                return (a * b) % modulus();
            }

            public long inv(long value) {
                long g = modulus(), x = 0, y = 1;
                for (long r = value; r != 0; ) {
                    long q = g / r;
                    g %= r;

                    long temp = g;
                    g = r;
                    r = temp;

                    x -= q * y;

                    temp = x;
                    x = y;
                    y = temp;
                }

                ASSERT(g == 1);
                ASSERT(y == modulus() || y == -modulus());

                return normalize(x);
            }

        }

        public static class Mod998 extends NumberTheory.Modulus<NumberTheory.Mod998> {
            public long modulus() {
                return 998_244_353L;
            }

        }

    }
}