#pragma once
#pragma GCC optimize("Ofast, unroll-loops")
#include<bits/stdc++.h>
#include"inv.h"
using std::cin;
using std::cout;
const int mod = 998244353;
const int mod2 = 974849; 
const int w = sqrt(mod2);
const int limit = 3 * (w + 1) * 1024;
int djq[limit], arr[mod2];
using u64 = unsigned long long;
int inv(int x) {
	const int p = (u64) x * arr[x >> 10] % mod;
	return (u64) arr[x >> 10] * (p < limit ? djq[p] : mod - djq[mod - p]) % mod;
}
void init(int) {
	for(int i = w;i >= 1;--i) {
		std::function<int(int)> getinv = [&](int x) {
			return x == 1 ? 1 : mod2 - u64(mod2 / x) * getinv(mod2 % x) % mod2;
		};
		int inv = getinv(i);
		for(int j = 1;j <= w;++j) {
			arr[(u64) j * inv % mod2] = i;
			arr[mod2 - (u64) j * inv % mod2] = mod - i;
		}
	}
	arr[0] = 1;
	// 0 <= x * arr[x] - k * mod2 < w, and arr[x] < w, k < w
	// 998244353 = mod2 * 1024 - 1023
	// 0 <= 1024x * arr[x] - k * 998244353 < w * 1024 + 1023 * k
	// 0 <= (1024x + y) * arr[x] - k * 998244353 < w * 1024 + 1023 * k + 1024 * w
	djq[1] = 1;
	// 等下再优化这个
	for(int i = 2;i < limit;++i) {
		djq[i] = mod - u64(mod / i) * djq[mod % i] % mod;
	}
}
/*
   int main() {
   std::ios::sync_with_stdio(false), cin.tie(0);
   init();
   for(int i = 1;i < mod;++i) {
   if(u64(getinv(i)) * i % mod != 1) {
   cout << getinv(i) << ' ' << i << '\n';
   return 0;
   }
   if(i % 300000 == 0) {
   std::cerr << "debug : " << i << std::endl;
   }

   }
   }
   */