Problem:
Score : 1200 points

Problem Statement

In Republic of AtCoder, Snuke Chameleons (Family: Chamaeleonidae, Genus: Bartaberia) are very popular pets.
Ringo keeps N Snuke Chameleons in a cage.

A Snuke Chameleon that has not eaten anything is blue. It changes its color according to the following rules:

A Snuke Chameleon that is blue will change its color to red when the number of red balls it has eaten becomes strictly larger than the number of blue balls it has eaten.

A Snuke Chameleon that is red will change its color to blue when the number of blue balls it has eaten becomes strictly larger than the number of red balls it has eaten.

Initially, every Snuke Chameleon had not eaten anything. Ringo fed them by repeating the following process K times:

Grab either a red ball or a blue ball.

Throw that ball into the cage. Then, one of the chameleons eats it.

After Ringo threw in K balls, all the chameleons were red. We are interested in the possible ways Ringo could have thrown in K balls. How many such ways are there? Find the count modulo 998244353. Here, two ways to throw in balls are considered different when there exists i such that the color of the ball that are thrown in the i-th throw is different.

Constraints

1 \leq N,K \leq 5 \times 10^5

N and K are integers.

Input

Input is given from Standard Input in the following format:

N K

Output

Print the possible ways Ringo could have thrown in K balls, modulo 998244353.

Sample Input 1

2 4

Sample Output 1

7

We will use R to represent a red ball, and B to represent a blue ball. There are seven ways to throw in balls that satisfy the condition: BRRR, RBRB, RBRR, RRBB, RRBR, RRRB and RRRR.

Sample Input 2

3 7

Sample Output 2

57

Sample Input 3

8 3

Sample Output 3

0

Sample Input 4

8 10

Sample Output 4

46

Sample Input 5

123456 234567

Sample Output 5

857617983

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.io.BufferedWriter;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.util.InputMismatchException;
import java.io.IOException;
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);
        OutputWriter out = new OutputWriter(outputStream);
        TaskE solver = new TaskE();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskE {
        public static final int mod = 998244353;
        int n;
        int k;
        long[] fact;
        long[] ifact;

        long comb(int n, int k) {
            if (k < 0 || k > n) return 0;
            return fact[n] * ifact[k] % mod * ifact[n - k] % mod;
        }

        public void solve(int testNumber, InputReader in, OutputWriter out) {
            n = in.nextInt();
            k = in.nextInt();
            if (k < n) {
                out.println(0);
                return;
            }
            long[][] x = Factorials.getFIF(500010, mod);
            fact = x[0];
            ifact = x[1];

            long ans = 0;
            for (int diff = k % 2; diff <= k; diff += 2) {
                int nr = (k + diff) / 2;
                int nb = k - nr;
                if (nr < n) continue;
                int eq = n - diff;
                ans += comb(nr + nb, nb);
                if (ans >= mod) ans -= mod;

                int drop = Math.min(nr - n, n - eq);

                if (drop >= 0) {
                    int r2 = (k - diff) / 2 - drop - 1;
                    int b2 = k - r2;
                    ans -= comb(r2 + b2, b2);
                    if (ans < 0) ans += mod;
                }
            }

            out.println(ans);
        }

    }

    static class Factorials {
        public static long[][] getFIF(int max, int mod) {
            long[] fact = new long[max];
            long[] ifact = new long[max];
            long[] inv = new long[max];
            inv[1] = 1;
            for (int i = 2; i < max; i++) {
                inv[i] = (mod - mod / i) * inv[mod % i] % mod;
            }
            fact[0] = 1;
            ifact[0] = 1;
            for (int i = 1; i < max; i++) {
                fact[i] = fact[i - 1] * i % mod;
                ifact[i] = ifact[i - 1] * inv[i] % mod;
            }
            return new long[][]{fact, ifact, inv};
        }

    }

    static class OutputWriter {
        private final PrintWriter writer;

        public OutputWriter(OutputStream outputStream) {
            writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
        }

        public OutputWriter(Writer writer) {
            this.writer = new PrintWriter(writer);
        }

        public void close() {
            writer.close();
        }

        public void println(long i) {
            writer.println(i);
        }

        public void println(int i) {
            writer.println(i);
        }

    }

    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1 << 16];
        private int curChar;
        private int numChars;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        public int read() {
            if (this.numChars == -1) {
                throw new InputMismatchException();
            } else {
                if (this.curChar >= this.numChars) {
                    this.curChar = 0;

                    try {
                        this.numChars = this.stream.read(this.buf);
                    } catch (IOException var2) {
                        throw new InputMismatchException();
                    }

                    if (this.numChars <= 0) {
                        return -1;
                    }
                }

                return this.buf[this.curChar++];
            }
        }

        public int nextInt() {
            int c;
            for (c = this.read(); isSpaceChar(c); c = this.read()) {
                ;
            }

            byte sgn = 1;
            if (c == 45) {
                sgn = -1;
                c = this.read();
            }

            int res = 0;

            while (c >= 48 && c <= 57) {
                res *= 10;
                res += c - 48;
                c = this.read();
                if (isSpaceChar(c)) {
                    return res * sgn;
                }
            }

            throw new InputMismatchException();
        }

        public static boolean isSpaceChar(int c) {
            return c == 32 || c == 10 || c == 13 || c == 9 || c == -1;
        }

    }
}