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 Java (OpenJDK 11.0.6) (judge verdict: Runtime Error)

import java.io.IOException;
import java.io.InputStream;
import java.util.Arrays;
import java.util.NoSuchElementException;
import java.util.Objects;
import java.util.Random;
import java.util.Scanner;

class BIT {
	long bit[] = new long[0];
	int N = 0;

	BIT(int n) {
		bit = new long[n + 1];
		N = n;
	}

	void add(int a, long w) {
		for (int x = a; x < N; x += (x & -x))
			bit[x] += w;
	}

	long sum(int a) {
		long ret = 0;
		for (int x = a; x > 0; x -= x & -x)
			ret += bit[x];
		return ret;
	}

	long modsum(int a, int mod) {
		long ret = 0;
		for (int x = a; x > 0; x -= x & -x) {
			ret += bit[x];
			ret %= mod;
		}
		return ret;
	}
}
class MODBIT {
	long bit[] = new long[0];
	int N = 0;
	int mod=0;
	MODBIT(int n,int m) {
		bit = new long[n + 1];
		N = n;
		mod=m;
	}

	void add(int a, long w) {
		for (int x = a; x < N; x += (x & -x)) {
			bit[x] += w;
			bit[x] %= mod;
		}
	}

	long modsum(int a, long mod2) {
		long ret = 0;
		for (int x = a; x > 0; x -= x & -x) {
			ret += bit[x];
			ret %= mod2;
		}
		return ret;
	}
}

class FastScanner {
	private final InputStream in = System.in;
	private final byte[] buffer = new byte[1024];
	private int ptr = 0;
	private int buflen = 0;

	private boolean hasNextByte() {
		if (ptr < buflen) {
			return true;
		} else {
			ptr = 0;
			try {
				buflen = in.read(buffer);
			} catch (IOException e) {
				e.printStackTrace();
			}
			if (buflen <= 0) {
				return false;
			}
		}
		return true;
	}

	private int readByte() {
		if (hasNextByte())
			return buffer[ptr++];
		else
			return -1;
	}

	private static boolean isPrintableChar(int c) {
		return 33 <= c && c <= 126;
	}

	public boolean hasNext() {
		while (hasNextByte() && !isPrintableChar(buffer[ptr]))
			ptr++;
		return hasNextByte();
	}

	public String next() {
		if (!hasNext())
			throw new NoSuchElementException();
		StringBuilder sb = new StringBuilder();
		int b = readByte();
		while (isPrintableChar(b)) {
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}

	public long nextLong() {
		if (!hasNext())
			throw new NoSuchElementException();
		long n = 0;
		boolean minus = false;
		int b = readByte();
		if (b == '-') {
			minus = true;
			b = readByte();
		}
		if (b < '0' || '9' < b) {
			throw new NumberFormatException();
		}
		while (true) {
			if ('0' <= b && b <= '9') {
				n *= 10;
				n += b - '0';
			} else if (b == -1 || !isPrintableChar(b)) {
				return minus ? -n : n;
			} else {
				throw new NumberFormatException();
			}
			b = readByte();
		}
	}

	public int nextInt() {
		long nl = nextLong();
		if (nl < Integer.MIN_VALUE || nl > Integer.MAX_VALUE)
			throw new NumberFormatException();
		return (int) nl;
	}

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

	public char nextchar() {
		return next().charAt(0);
	}
}

class UnionFind {
	int Parent[];

	UnionFind(int n) {// Initialize by -1
		Parent = new int[n];
		Arrays.fill(Parent, -1);
	}

	int root(int A) {// In which tree is A?
		if (Parent[A] < 0)
			return A;
		return Parent[A] = root(Parent[A]);
	}

	int size(int A) {// size of tree which is include A
		return -Parent[root(A)];
	}

	boolean connect(int A, int B) {// Connect A and B
		A = root(A);
		B = root(B);
		if (A == B)
			return false;
		if (size(A) < size(B)) {
			int C = 0;
			C = B;
			B = A;
			A = C;
		} // SWAP
		Parent[A] += Parent[B];
		Parent[B] = A;
		return true;
	}
}

class Pair<T, E> {
	public T first;
	public E second;

	void set(T x, E y) {
		first = x;
		second = y;
	}
}

class Pint {
	@Override
	public boolean equals(Object obj) {
		if (obj instanceof Pint) {
			Pint other = (Pint) obj;
			return other.first == this.first && other.second == this.second;
		}
		return false;
	}

	@Override
	public int hashCode() {
		return Objects.hash(this.first, this.second);
	}

	public int first;
	public int second;

	Pint(int x, int y) {
		first = x;
		second = y;
	}

	void set(int x, int y) {
		first = x;
		second = y;
	}
}

class Tpair {
	public int first;
	public int second;
	public long third;

	Tpair(int x, int y, long z) {
		first = x;
		second = y;
		third = z;
	}

	void set(int x, int y, long z) {
		first = x;
		second = y;
		third = z;
	}
}
class Comb{
	int N=0;
	int mod=0;
	long fact[],ifact[],inv[];
	Comb(int n,int m){
		N=n;
		mod=m;
		fact=new long[N+10];
		ifact=new long[N+10];
		inv=new long[N+10];
		inv[1] = 1;
		for (int i = 2; i < N; i++) inv[i] = 1l * (mod - mod / i) * inv[mod % i] % mod;
		fact[0] = ifact[0] = 1;
		for (int i = 1; i < N; i++) {
			fact[i] = 1l * fact[i - 1] * i % mod;
			ifact[i] = 1l * ifact[i - 1] * inv[i] % mod;
		}
	}
	public long C(int x,int y,long mod) {
		if (x < 0 || y < 0 || x < y) return 0;
		return 1l * fact[x] * ifact[y] % mod * ifact[x - y] % mod;
	}
}
public class Main {
	static FastScanner scan = new FastScanner();
	static Scanner scanner = new Scanner(System.in);
	static Random rand = new Random();
	static int mod = 1000000007;
	static double eps = 1.0E-14;
	static int big = Integer.MAX_VALUE;
	static double PI = 3.141592653589793;

	static long modlcm(long a, long b) {
		return a * b * modinv(GCD(a, b), mod);
	}

	static long GCD(long a, long b) {
		return b > 0 ? GCD(b, a % b) : a;
	}

	static long lcm(long a, long b) {
		return a * b / GCD(a, b);
	}

	static int min(int a, int b) {
		return a < b ? a : b;
	}

	static long factorial(int i) {
		return i == 1 ? 1 : i * factorial(i - 1);
	}

	static int max(int... i) {
		int x = i[0];
		for (int e : i)
			x = Math.max(x, e);
		return x;
	}

	static int min(int... i) {
		int x = i[0];
		for (int e : i)
			x = Math.min(x, e);
		return x;
	}

	static long gcd(long... i) {
		long x = i[0];
		for (long e : i)
			x = GCD(x, e);
		return x;
	}

	static long lmax(long... i) {
		long x = i[0];
		for (long e : i)
			x = Math.max(x, e);
		return x;
	}

	static long lmin(long... i) {
		long x = i[0];
		for (long e : i)
			x = Math.min(x, e);
		return x;
	}

	static long nCr(long n, long r, long m) {
		long ans = 1;
		for (long i = 0; i < r; i++) {
			ans *= (n - i);
			ans %= m;
		}
		for (long i = 0; i <= r; i++) {
			ans *= modinv(i, m);
			ans %= mod;
		}
		return ans;
	}

	static int lower_bound(long[] b, long cost) {
		int ok = b.length;
		int ng = -1;
		while (Math.abs(ok - ng) > 1) {
			int mid = (ok + ng) / 2;
			if (b[mid] >= cost)
				ok = mid;
			else
				ng = mid;
		}
		return ok;
	}

	static int upper_bound(int[] b, int cost) {
		int ok = b.length;
		int ng = -1;
		while (Math.abs(ok - ng) > 1) {
			int mid = (ok + ng) / 2;
			if (b[mid] > cost)
				ok = mid;
			else
				ng = mid;
		}
		return ok;
	}

	static boolean isPrime(long n) {
		if (n == 2)
			return true;
		if (n < 2 || n % 2 == 0)
			return false;
		double d = Math.sqrt(n);
		for (int i = 3; i <= d; i += 2)
			if (n % i == 0) {
				return false;
			}
		return true;
	}

	static int upper_division(int a, int b) {
		if (a % b == 0) {
			return a / b;
		} else {
			return a / b + 1;
		}
	}

	static long lupper_division(long a, long b) {
		if (a % b == 0) {
			return a / b;
		} else {
			return a / b + 1;
		}
	}

	static int[] setArray(int a) {
		int b[] = new int[a];
		for (int i = 0; i < a; i++) {
			b[i] = scan.nextInt();
		}
		return b;
	}

	static long[] lsetArray(int a) {
		long b[] = new long[a];
		for (int i = 0; i < a; i++) {
			b[i] = scan.nextLong();
		}
		return b;
	}

	static String reverse(String str) {
		char ch[] = new char[str.length()];
		char chch[] = str.toCharArray();
		int a = str.length();
		for (int i = 0; i < upper_division(a, 2); i++) {
			ch[i] = chch[ch.length - i - 1];
			ch[ch.length - 1 - i] = chch[i];
		}
		return String.valueOf(ch);
	}

	public static void printArray(int[] que) {
		for (int i = 0; i < que.length - 1; i++) {
			System.out.print(que[i] + " ");
		}
		System.out.println(que[que.length - 1]);
	}

	public static void lprintArray(long[] que) {
		for (int i = 0; i < que.length - 1; i++) {
			System.out.print(que[i] + " ");
		}
		System.out.println(que[que.length - 1]);
	}

	public static int[][] doublesort(int[][] a) {
		Arrays.sort(a, (x, y) -> Integer.compare(x[0], y[0]));
		return a;
	}

	public static long[][] ldoublesort(long[][] a) {
		Arrays.sort(a, (x, y) -> Long.compare(x[0], y[0]));
		return a;
	}

	static long modpow(long x, long n, long mo) {
		long sum = 1;
		while (n > 0) {
			if ((n & 1) == 1) {
				sum = sum * x % mo;
			}
			x = x * x % mo;
			n >>= 1;
		}
		return sum;
	}

	public static char[] revch(char ch[]) {
		char ret[] = new char[ch.length];
		for (int i = ch.length - 1, j = 0; i >= 0; i--, j++) {
			ret[j] = ch[i];
		}
		return ret;
	}

	public static int[] revint(int ch[]) {
		int ret[] = new int[ch.length];
		for (int i = ch.length - 1, j = 0; i >= 0; i--, j++) {
			ret[j] = ch[i];
		}
		return ret;
	}

	public static void warshall_floyd(long v[][]) {
		int n = v[0].length;
		for (int k = 0; k < n; k++)
			for (int i = 0; i < n; i++)
				for (int j = 0; j < n; j++)
					v[i][j] = lmin(v[i][j], v[i][k] + v[k][j]);
	}

	public static long modinv(long a, long m) {
		long b = m, u = 1, v = 0;
		while (b != 0) {
			long t = a / b;
			a -= t * b;
			long x = a;
			a = b;
			b = x;
			u -= t * v;
			x = u;
			u = v;
			v = x;
		}
		u %= m;
		if (u < 0)
			u += m;
		return u;
	}

	public static long lmod(long i, long j) {
		return (i % j) < 0 ? (i % j) + 0 + (j < 0 ? -j : j) : (i % j + 0);
	}

	public static int next_combination(int sub) {
		int x = sub & -sub, y = sub + x;
		return (((sub & ~y) / x) >> 1) | y;
	}
	public static void main(String[] $) throws IOException {
		mod=998244353;
		Comb comb=new Comb(50040,mod);
		int n=scan.nextInt();
		int m=scan.nextInt();
		long ans=0;
		for(int r=m;r>=n&&r>=m-r;r--) {
			int f=(r==(m-r))?1:0;
			ans = (ans + (comb.C(m - f, r,mod) - comb.C(m - f, 2 * r - n + 1,mod) + mod) % mod) % mod;
		}
		System.out.println(ans);
	}
}