#include<bits/stdc++.h>
#include "inv.h"
#define L(i, j, k) for(int i = (j); i <= (k); ++i)
#define R(i, j, k) for(int i = (j); i >= (k); --i)
#define ll long long 
#define vi vector < int > 
#define sz(a) ((int) (a).size())
#define ll long long 
#define ull unsigned long long
#define me(a, x) memset(a, x, sizeof(a)) 
#define eb emplace_back
using namespace std;
const int B = 1e3, buf = 3, mod = 998244353, N = 6e6 + 7;
int K, ml[N], iv[N];
int Inv(int x) {
	return x < N ? iv[x] : (ll) Inv(mod % x) * (mod - mod / x) % mod;
}
int inv(int w) {
	int d = w / B;
	return !ml[d] ? Inv(w) : (ll) iv[(ll) w * ml[d] % mod] * ml[d] % mod;
} 
void init(int rp) {
	K = mod / B;
	L(fb, 1, B * buf) {
		int cur = 0;
		for(int p = 0; p <= K; ++p) {
			if(cur <= K * buf) {
				ml[p] = fb;
			}
			cur += fb * B;
			if(cur >= mod) cur -= mod;
		}
	}
	iv[1] = 1;
	L(i, 2, N - 1) iv[i] = (ll) iv[mod % i] * (mod - mod / i) % mod;
}