#include<bits/stdc++.h>
// #include "inv.h"
#define rep(i,l,r) for (int i(l), i##end(r); i <= i##end; ++i)
#define per(i,r,l) for (int i(r), i##end(l); i >= i##end; --i)
using namespace std;

const int N = 1e8 + 9, Mod = 998244353;
int n = N - 9, MMI[N];
void init(int p) {
	MMI[1] = 1;
	rep (i, 2, n) MMI[i] = Mod - 1ll * (Mod / i) * MMI[Mod % i] % Mod;
}
int inv(int x) {
	if (x <= n) return MMI[x];
	int q = Mod / x, r = Mod % x;
	if (r < x / 2) return Mod - 1ll * q * inv(r) % Mod;
	return 1ll * (q + 1) * inv(x - r) % Mod;
}