Submission #72408015

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Source Code Expand

#include<bits/stdc++.h>
using namespace std;
#define IOS ios::sync_with_stdio(false), cin.tie(nullptr), cout.tie(nullptr)
using LL = long long;
using pii = pair<int, int>;
#define fi first
#define se second
constexpr int MAXN = 2e7 + 5, mod = 998244353;
inline void inc(int &x, int y) { (x += y) >= mod && (x -= mod); }
inline void dec(int &x, int y) { (x -= y) < 0 && (x += mod); }
inline void tim(int &x, int y) { x = (LL)x * y % mod; }
inline int madd(int x, int y) { return x + y >= mod ? x + y - mod : x + y; }
inline int msub(int x, int y) { return x - y < 0 ? x - y + mod : x - y; }
inline int mmul(int x, int y) { return (LL)x * y % mod; }
inline int qpow(int x, int y = mod - 2) {
	int ret = 1;
	while (y) {
		if (y & 1) tim(ret, x);
		tim(x, x), y >>= 1;
	}
	return ret;
}
int n, m, fac[MAXN], invf[MAXN];
inline int binom(int N, int M) {
	if (N < M || N < 0 || M < 0) return 0;
	return (LL)fac[N] * invf[M] % mod * invf[N - M] % mod;
}
inline int calc(int N, int M) {
	return binom(N + M - 1, M * 2 - 1);
}
int main() {
	IOS;
	cin >> n >> m;
	if (n < m) {
		cout << "0\n";
		return 0;
	}
	fac[0] = 1;
	for (int i = 1; i <= n + m; ++i) fac[i] = mmul(fac[i - 1], i);
	invf[n + m] = qpow(fac[n + m]);
	for (int i = n + m; i >= 1; --i) invf[i - 1] = mmul(invf[i], i);
	int ans = 0;
	for (int i = 0; i <= n; ++i) {
		int j = n - i;
		if (i < j) continue;
		inc(ans, (LL)binom(j + m - 1, m - 1) * calc(i - j, m) % mod);
	}
	cout << mmul(ans, qpow(2, m));
	return 0;
}

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