Problem: 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.

Examples

Input

2 4


Output

7


Input

3 7


Output

57


Input

8 3


Output

0


Input

8 10


Output

46


Input

123456 234567


Output

857617983

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.*;

public class Main {

	static final int P = 998244353;

	ModuloCombinatorics mc = new ModuloCombinatorics(1000000, P);

	int solve(int n, int k) {
		// System.err.println(n + " " + k);
		int ans = 0;

		for (int plus = 0; plus <= k; plus++) {
			int minus = k - plus;
			if (plus < minus || plus < n) {
				continue;
			}
			int same = Math.max(n - (plus - minus), 0);
			if (same > minus) {
				throw new AssertionError();
			}

			int maxNeg = minus - same;
			ans += go(plus, plus == minus ? minus - 1 : minus, maxNeg);
			if (ans >= P) {
				ans -= P;
			}
		}
		return ans;
	}

	int go(int p, int q, int bad) {
		int newSum = p + q;
		int newDiff = -2 * (bad + 1) - (p - q);
		int x = (newSum + newDiff) / 2;
		int y = (newSum - newDiff) / 2;
		int ret = mc.choose(p + q, p);
		if (x >= 0 && y >= 0) {
			ret -= mc.choose(x + y, x);
			if (ret < 0) {
				ret += P;
			}
		}
		return ret;
	}

	void submit() {
		out.println(solve(nextInt(), nextInt()));
	}

	static class ModuloCombinatorics {
		/** maximal needed number, N itself is included **/
		final int N;

		/** prime modulo **/
		final int P;

		/** factorials **/
		final int[] fact;

		/** multiplicative inverses, take care to not touch inv[0] **/
		final int[] inv;

		/** inverse factorials **/
		final int[] invFact;

		public ModuloCombinatorics(int N, int P) {
			this.N = N;
			this.P = P;
			fact = new int[N + 1];
			fact[0] = 1;
			for (int i = 1; i <= N; i++) {
				fact[i] = (int) ((long) i * fact[i - 1] % P);
			}

			inv = new int[N + 1];
			inv[1] = 1;
			for (int i = 2; i <= N; i++) {
				inv[i] = P - (int) ((long) (P / i) * inv[P % i] % P);
			}

			invFact = new int[N + 1];
			invFact[0] = 1;
			for (int i = 1; i <= N; i++) {
				invFact[i] = (int) ((long) invFact[i - 1] * inv[i] % P);
			}
		}

		public int choose(int n, int k) {
			return (n < 0 || k < 0 || k > n) ? 0 : (int) ((long) fact[n]
					* invFact[k] % P * invFact[n - k] % P);
		}

		/** a^b modulo mod, mod is arbitrary **/
		static public int pow(int a, long b, int mod) {
			if (a < 0 || a >= mod || b < 0) {
				throw new IllegalArgumentException();
			}
			int ret = 1;
			for (; b > 0; b >>= 1) {
				if ((b & 1) == 1) {
					ret = (int) ((long) ret * a % mod);
				}
				a = (int) ((long) a * a % mod);
			}
			return ret;
		}

		/** a^b modulo P **/
		public int pow(int a, long b) {
			return pow(a, b, P);
		}
	}

	void preCalc() {

	}

	void stress() {

	}

	void test() {
		solve(1, 3);
		for (int n = 1; n <= 10; n++) {
			for (int k = 1; k <= 10; k++) {
				solve(n, k);
			}
		}
	}

	Main() throws IOException {
		br = new BufferedReader(new InputStreamReader(System.in));
		out = new PrintWriter(System.out);
		preCalc();
		submit();
		// stress();
		// test();
		out.close();
	}

	static final Random rng = new Random();

	static int rand(int l, int r) {
		return l + rng.nextInt(r - l + 1);
	}

	public static void main(String[] args) throws IOException {
		new Main();
	}

	BufferedReader br;
	PrintWriter out;
	StringTokenizer st;

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

	String nextString() {
		try {
			return br.readLine();
		} catch (IOException e) {
			throw new RuntimeException(e);
		}
	}

	int nextInt() {
		return Integer.parseInt(nextToken());
	}

	long nextLong() {
		return Long.parseLong(nextToken());
	}

	double nextDouble() {
		return Double.parseDouble(nextToken());
	}
}