This documentation is automatically generated by competitive-verifier/competitive-verifier
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
#define rep(i, n) for (int i = 0; i < n; i++)
#define all(v) v.begin(), v.end()
template <class T, class U>
inline bool chmax(T& a, U b) {
if (a < b) {
a = b;
return true;
}
return false;
}
template <class T, class U>
inline bool chmin(T& a, U b) {
if (a > b) {
a = b;
return true;
}
return false;
}
constexpr int INF = 1000000000;
constexpr ll llINF = 3000000000000000000;
constexpr int mod = 998244353;
constexpr double eps = 1e-10;
vector<int> calc_factor(int n) {
vector<int> least_factor(n + 1, 0), prime_list;
for (int i = 2; i <= n; i++) {
if (least_factor[i] == 0) {
least_factor[i] = i;
prime_list.push_back(i);
}
for (int j = 0; j < (int)prime_list.size() && i * prime_list[j] <= n; j++) {
least_factor[i * prime_list[j]] = prime_list[j];
if (prime_list[j] == least_factor[i]) break;
}
}
return least_factor;
}
ll modpow(ll a, ll b, ll m = mod) {
ll res = 1;
while (b) {
if (b & 1) {
res *= a;
res %= m;
}
a *= a;
a %= m;
b >>= 1;
}
return res;
}
vector<ll> inv, fact, factinv;
void init_fact(int n) {
inv.resize(n + 1);
fact.resize(n + 1);
factinv.resize(n + 1);
inv[0] = 0;
inv[1] = 1;
fact[0] = 1;
factinv[0] = 1;
for (ll i = 1; i <= n; i++) {
if (i >= 2) inv[i] = mod - ((mod / i) * inv[mod % i] % mod);
fact[i] = (fact[i - 1] * i) % mod;
factinv[i] = factinv[i - 1] * inv[i] % mod;
}
}
ll modinv(ll a, ll m = mod) {
ll b = m, u = 1, v = 0;
while (b) {
ll t = a / b;
a -= t * b;
swap(a, b);
u -= t * v;
swap(u, v);
}
u %= m;
if (u < 0) u += m;
return u;
}
ll comb(int a, int b) {
if (a < b) return 0;
if (a < 0) return 0;
return fact[a] * factinv[a - b] % mod * factinv[b] % mod;
}
int main() {
cin.tie(0);
ios::sync_with_stdio(false);
}
#line 1 "template_old.cpp"
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
#define rep(i, n) for (int i = 0; i < n; i++)
#define all(v) v.begin(), v.end()
template <class T, class U>
inline bool chmax(T& a, U b) {
if (a < b) {
a = b;
return true;
}
return false;
}
template <class T, class U>
inline bool chmin(T& a, U b) {
if (a > b) {
a = b;
return true;
}
return false;
}
constexpr int INF = 1000000000;
constexpr ll llINF = 3000000000000000000;
constexpr int mod = 998244353;
constexpr double eps = 1e-10;
vector<int> calc_factor(int n) {
vector<int> least_factor(n + 1, 0), prime_list;
for (int i = 2; i <= n; i++) {
if (least_factor[i] == 0) {
least_factor[i] = i;
prime_list.push_back(i);
}
for (int j = 0; j < (int)prime_list.size() && i * prime_list[j] <= n; j++) {
least_factor[i * prime_list[j]] = prime_list[j];
if (prime_list[j] == least_factor[i]) break;
}
}
return least_factor;
}
ll modpow(ll a, ll b, ll m = mod) {
ll res = 1;
while (b) {
if (b & 1) {
res *= a;
res %= m;
}
a *= a;
a %= m;
b >>= 1;
}
return res;
}
vector<ll> inv, fact, factinv;
void init_fact(int n) {
inv.resize(n + 1);
fact.resize(n + 1);
factinv.resize(n + 1);
inv[0] = 0;
inv[1] = 1;
fact[0] = 1;
factinv[0] = 1;
for (ll i = 1; i <= n; i++) {
if (i >= 2) inv[i] = mod - ((mod / i) * inv[mod % i] % mod);
fact[i] = (fact[i - 1] * i) % mod;
factinv[i] = factinv[i - 1] * inv[i] % mod;
}
}
ll modinv(ll a, ll m = mod) {
ll b = m, u = 1, v = 0;
while (b) {
ll t = a / b;
a -= t * b;
swap(a, b);
u -= t * v;
swap(u, v);
}
u %= m;
if (u < 0) u += m;
return u;
}
ll comb(int a, int b) {
if (a < b) return 0;
if (a < 0) return 0;
return fact[a] * factinv[a - b] % mod * factinv[b] % mod;
}
int main() {
cin.tie(0);
ios::sync_with_stdio(false);
}