#include "inv.h"
#include <bits/stdc++.h>
using namespace std;
const int B = 1 << 10, T = 1 << 20, P = 998244353;
int f[T+1], p[T+1], buf[T*3+3], * I = buf + T;
void init(int) {
	for (int i=1; i<=B; i++) {
		int s = 0, d = i << 10;
		for (int j=1; j<=T; j++) {
			if ((s += d) >= P) s -= P;
			if (s <= T) {
				if (! f[j]) f[j] = i, p[j] = s;
			} else if (s >= P - T) {
				if (! f[j]) f[j] = i, p[j] = s - P;
			} else {
				int t = (P - T - s - 1) / d;
				s += t * d, j += t;
			}
		}
	}
	I[1] = f[0] = 1;
	for (int i=2; i<=T<<1; i++)
		I[i] = 1ll * (P - P / i) * I[P%i] % P;
	for (int i=-1; i>=-T; i--)
		I[i] = P - I[-i];
}
int inv(int x) {
	return 1ll * I[p[x>>10]+(x&1023)*f[x>>10]] * f[x>>10] % P;
}