#pragma GCC optimize("Ofast,unroll-loops")

const int mod = 998244353;
const int pre = 5e6;

int a[pre];

void init(int p) {
	a[0] = a[1] = 1;
	for (int i = 2; i < pre; i++) {
		a[i] = 1ll * (mod - mod / i) * a[mod % i] % mod;
	}
}

int inv(int x) {
	if (x < pre) return a[x];
	int ret = 1;
	while (x >= pre) {
		ret = 1ll * ret * (mod - mod / x) % mod;
		x = mod % x;
	}
	ret = 1ll * ret * a[x] % mod;	
	return ret;
}