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 C (GCC 9.2.1) (judge verdict: Accepted)

#if 0
cat <<EOF >mistaken-paste
#endif
// thx Ebi-chan!

// #pragma GCC optimize("unroll-loops")
// #pragma GCC optimize("O3")

#pragma GCC diagnostic ignored "-Wincompatible-pointer-types"
#define _USE_MATH_DEFINES

#include <stdio.h>
#include <stdint.h>
#include <stdlib.h>
#include <string.h>
#include <stdbool.h>
#include <math.h>
#include <time.h>

#define BIG 2000000007LL
#define VERYBIG 200000000000000007LL
#define ULTRABIG 300000000000000000000LL

#define MOD 1000000007LL
#define FOD  998244353LL
#define HOD 1000000009LL
#define IOD  100000007LL
typedef uint64_t ull;
typedef  int64_t sll;

#define N_MAX 1048576

#ifdef __cplusplus
#include <queue>
#include <stack>
// #include <tuple>
#include <set>
#include <map>
#include <string>
#include <algorithm>
// #include <functional>
// #include <array>
#include <iostream>

using std::queue;
using std::priority_queue;
using std::stack;
// using std::tuple;
using std::set;
using std::map;
using std::vector;
using std::greater;
using std::pair;
using std::string;
// using std::get;
// using std::function;
// using std::array;
using std::cin;
using std::cout;
using std::endl;

template <typename T, typename U>
pair<T, U> operator+(pair<T, U> l, pair<T, U> r) {
	return pair<T, U>(l.first + r.first, l.second + r.second);
}

#endif

#ifndef M_PI
#define M_PI 3.14159265358979323846264338327950
#endif

typedef struct {
	sll a;
	sll b;
} hwll;

typedef struct {
	sll a;
	sll b;
	sll c;
} hwllc;

typedef struct {
	hwll a;
	hwll b;
} linell;

typedef struct {
	double a;
	double b;
} hwreal;

sll n, m;
sll h, w;
sll k;
sll q;
sll va, vb, vc, vd, ve, vf;
ull ua, ub, uc, ud, ue, uf;
long double vra, vrb, vrc;
double vda, vdb, vdc;
char ch, dh;

ull umin (ull x, ull y) {
	return (x < y) ? x : y;
}

ull umax (ull x, ull y) {
	return (x > y) ? x : y;
}

sll smin (sll x, sll y) {
	return (x < y) ? x : y;
}

sll smax (sll x, sll y) {
	return (x > y) ? x : y;
}

double dmin (double x, double y) {
	return (x < y) ? x : y;
}

double dmax (double x, double y) {
	return (x > y) ? x : y;
}

ull gcd (ull x, ull y) {
	if (y == 0) {
		return x;
	} else {
		return gcd(y, x % y);
	}
}

ull bitpow (ull a, ull x, ull modulo) {
	ull result = 1;
	while (x) {
		if (x & 1) {
			result *= a;
			result %= modulo;
		}
		x /= 2;
		a = (a * a) % modulo;
	}
	return result;
}

ull divide (ull a, ull b, ull modulo) {
	return (a * bitpow(b, modulo - 2, modulo)) % modulo;
}

ull udiff (ull a, ull b) {
	if (a >= b) {
		return a - b;
	} else {
		return b - a;
	}
}

sll sdiff (sll a, sll b) {
	if (a >= b) {
		return a - b;
	} else {
		return b - a;
	}
}

int bitcount (ull n) {
	int result = 0;
	while (n) {
		if (n & 1) result++;
		n /= 2;
	}
	return result;
}

#define BEGCMP(NAME) int32_t NAME (const void *left, const void *right)
#define DEFLR(TYPE) TYPE l=*(TYPE*)left,r=*(TYPE*)right
#define CMPRET(L, R) if((L)<(R))return-1;if((L)>(R))return+1

// int32_t pullcomp (const void *left, const void *right) {
// 	ull l = *(ull*)left;
// 	ull r = *(ull*)right;
// 	if (l < r) {
// 		return -1;
// 	}
// 	if (l > r) {
// 		return +1;
// 	}
// 	return 0;
// }
BEGCMP(pullcomp){
	DEFLR(ull);
	CMPRET(l, r);
	return 0;
}
BEGCMP(prevcomp){
	DEFLR(sll);
	CMPRET(r, l);
	return 0;
}
BEGCMP(psllcomp){
	DEFLR(sll);
	CMPRET(l, r);
	return 0;
}
BEGCMP(pcharcomp){
	DEFLR(char);
	CMPRET(l, r);
	return 0;
}
BEGCMP(pdoublecomp){
	DEFLR(double);
	CMPRET(l, r);
	return 0;
}

int32_t pstrcomp (const void *left, const void *right) {
	char* l = *(char**)left;
	char* r = *(char**)right;

	return strcmp(l, r);
}

BEGCMP(phwllABcomp){
	DEFLR(hwll);
	CMPRET(l.a, r.a);
	CMPRET(l.b, r.b);
	return 0;
}
BEGCMP(phwllREVcomp){
	DEFLR(hwll);
	CMPRET(l.b, r.b);
	CMPRET(l.a, r.a);
	return 0;
}
BEGCMP(ptriplecomp){
	DEFLR(hwllc);
	CMPRET(l.a, r.a);
	CMPRET(l.b, r.b);
	CMPRET(l.c, r.c);
	return 0;
}
BEGCMP(ptripleREVcomp){
	DEFLR(hwllc);
	CMPRET(l.b, r.b);
	CMPRET(l.a, r.a);
	CMPRET(l.c, r.c);
	return 0;
}
BEGCMP(ptripleCABcomp){
	DEFLR(hwllc);
	CMPRET(l.c, r.c);
	CMPRET(l.a, r.a);
	CMPRET(l.b, r.b);
	return 0;
}
BEGCMP(phwrealcomp){
	DEFLR(hwreal);
	CMPRET(l.a, r.a);
	CMPRET(l.b, r.b);
	return 0;
}

int32_t pquadcomp (const void *left, const void *right) {
	linell l = *(linell*)left;
	linell r = *(linell*)right;

	sll ac = phwllABcomp(&(l.a), &(r.a));
	if (ac) return ac;
	sll bc = phwllABcomp(&(l.b), &(r.b));
	if (bc) return bc;

	return 0;
}
int32_t pfracomp (const void *left, const void *right) {
	hwll l = *(hwll*)left;
	hwll r = *(hwll*)right;

	CMPRET(l.a * r.b, l.b * r.a);
	return 0;
}
bool isinrange (sll left, sll x, sll right) {
	return (left <= x && x <= right);
}

bool isinrange_soft (sll left, sll x, sll right) {
	return (left <= x && x <= right) || (left >= x && x >= right);
}

void sw (sll *l, sll *r) {
	if (*l == *r) return;
	sll t = *l;
	*l = *r;
	*r = t;
}

void uw (ull *l, ull *r) {
	if (*l == *r) return;
	ull t = *l;
	*l = *r;
	*r = t;
}

ull frac[N_MAX * 10], invf[N_MAX * 10];
void f_init (sll n, sll m) {
	frac[0] = 1;
	for (sll i = 1; i <= n; i++) {
		frac[i] = frac[i - 1] * i % m;
	}

	invf[n] = divide(1, frac[n], m);
	for (sll i = n - 1; i >= 0; i--) {
		invf[i] = invf[i + 1] * (i + 1) % m;
	}
}
ull ncr (sll n, sll r, ull m) {
	if (n < 0 || r < 0 || n < r) return 0;
	return frac[n] * (invf[r] * invf[n - r] % m) % m;
}

sll a[N_MAX * 10];
// ull a[N_MAX + 5];
// sll a[3001][3001];
sll b[N_MAX * 5];
// ull b[N_MAX + 5];
// sll b[3001][3001];
sll c[N_MAX * 5];
sll d[N_MAX * 5];
sll e[N_MAX * 4];
char s[N_MAX + 1];
// char s[3010][3010];
char t[N_MAX + 1];
// char t[3010][3010];
char u[N_MAX + 1];
hwll xy[N_MAX * 4];
hwllc tup[N_MAX * 4];
// sll table[3005][3005];
sll table[2005][2005];
ull gin[N_MAX];
// here we go

ull parent[501910], size[501910], edges[501910];
void init (ull n) {
	for (sll i = 0; i < n; i++) {
		parent[i] = i;
		size[i] = 1;
	}
}
ull find (ull x) {
	if (parent[x] == x) return x;
	return parent[x] = find(parent[x]);
}
bool unite (ull v, ull u) {
	v = find(v);
	u = find(u);



	if (v == u) return false;

	if (size[v] < size[u]) {
		ull tmp = v;
		v = u;
		u = tmp;
	}
	size[v] += size[u];
	parent[u] = v;
	return true;
}

// typedef pair<sll, sll> P;

sll yuri (sll n, sll k, sll s) {
	return FOD + ncr(n, k, FOD) - ncr(n, k + s + 1, FOD);
}

sll solve () {
	sll i, j, ki, li;
	// ull result = 0;
	sll result = 0;
	double dresult = 0;
	// ull maybe = 0;
	sll maybe = 0;
	// ull sum = 0;
	sll sum = 0;
	sll item;
	sll *dpcell;

	f_init(k * 2, FOD);

	sll blue, red;
	for (blue = n; blue <= k; blue++) {
		red = k - blue;

		if (blue < red) continue;
		if (blue - red >= n) {
			result += ncr(k, blue, FOD);
			// printf("%lld..\n", result);
			continue;
		}
		sll s = blue - n;
		if (blue > red) {
			result += yuri(k, blue, s);
		} else {
			result += yuri(k - 1, blue, s);
		}
			// printf("%lld...\n", result);

	}
	result %= FOD;

	printf("%lld\n", result);
	// printf("%.15f\n", dresult);
	// puts(s);

	return 0;

	success:
	// puts("YES");
	puts("Yes");
	// printf("%lld\n", result);
	// puts("0");
	// puts("First");
	return 0;

	fail:
	// puts("NO");
	puts("No");
	// puts("0");
	// puts("-1");
	// puts("-1 -1 -1");
	// puts(":(");
	return 1;
}

int32_t main (int argc, char *argv[]) {
	int32_t i, j;

	n = 3;
	m = 0;
	h = 5;

	// scanf("%llu", &m);
	// scanf("%lld", &w);
	// scanf("%lld%lld", &h, &w);
	scanf("%lld", &n, &m);
	// scanf("%lld", &k, &n, &m);
	// scanf("%llu%llu", &h, &w);
	// scanf("%lld", &q);
	// scanf("%lld%lld%lld", &va, &vb, &vc, &vd);
	// va--;
	// vb--;
	// scanf("%llu%llu%llu%llu", &ua, &ub, &uc, &ud, &ue);
	// scanf("%s", s);
	// scanf("%s", t);
	// scanf("%s", u);
	scanf("%lld", &k);
	// scanf("%lld", &m);
	// scanf("%lld", &n);
	// for (i = 0; i < n; i++) {
	// 	// scanf("%s", s[i]);
	// 	scanf("%lld", &c[i]);
	// }
	// scanf(" %c", &ch);
	// scanf("%llu", &q);
	for (i = 0; i < 0; i++) {

		// scanf("%lld%lld", &xy[i].a, &xy[i].b);
		// scanf("%lld%lld%lld", &tup[i].a, &tup[i].b, &tup[i].c);
		// scanf("%lld", &c[i]);

		scanf("%lld", &a[i]);
		// scanf("%lld", &b[i]);
		// scanf("%lld", &c[i]);
		// scanf("%lld", &d[i]);
		// scanf("%lld", &e[i]);
		// a[i]--;
		// b[i]--;
		// c[i]--;
		// d[i]--;
		// xy[i].a--;
		// xy[i].b--;
		// tup[i].a--;
		// tup[i].b--;
	}
	// scanf("%lld%lld", &va, &vb);
	// scanf("%llu", &m);
	// scanf("%llu", &q);
	// scanf("%s", t);
	// for (i = 0; i < n; i++) {
	// 	// scanf("%lld%lld", &xy[i].a, &xy[i].b);
	// 	// xy[i].a--;
	// 	// xy[i].b--;
	// 	// scanf("%lld", &a[i], &b[i]);
	// 	// scanf("%lld", &b[i]);
	// 	// a[i]--;
	// 	// b[i]--;
	// 	scanf("%lld", &c[i]);
	// 	// scanf("%lld", &d[i]);
	// 	// scanf("%lld", &e[i]);
	// 	c[i]--;
	// 	// d[i]--;
	// }

	// for (i = 0; i < q; i++) {
	// 	// scanf("%lld%lld", &xy[i].a, &xy[i].b);
	// 	scanf("%lld", &c[i]);
	// 	// xy[i].a--;
	// 	// xy[i].b--;
	// }

	// for (i = 0; i < h; i++) {
	// 	for (j = 0; j < w; j++) {
	// 		scanf("%lld", &table[i][j]);
	// 		// table[i][j]--;
	// 	}
	// }
	// for (i = 0; i < n; i++) {
	// 	scanf("%s", s[i]);
	// }
	// for (i = 0; i < n; i++) {
	// 	scanf("%s", t[i]);
	// }
	// scanf("%llu", &q);
	// for (i = 0; i < q; i++) {
	// 	scanf("%lld%lld%lld", &e[i], &c[i], &d[i]);
	// 	c[i]--;
	// }

	solve();

	return 0;
}