結果
| 問題 |
No.3026 Range LCM (Online Version)
|
| ユーザー |
 Rubikun
|
| 提出日時 | 2025-02-14 23:13:34 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
TLE
|
| 実行時間 | - |
| コード長 | 31,840 bytes |
| コンパイル時間 | 5,192 ms |
| コンパイル使用メモリ | 271,408 KB |
| 実行使用メモリ | 941,912 KB |
| 最終ジャッジ日時 | 2025-02-14 23:20:06 |
| 合計ジャッジ時間 | 90,156 ms |
|
ジャッジサーバーID （参考情報） |
judge4 / judge2 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 1 |
| other | AC * 21 TLE * 14 MLE * 1 |
コンパイルメッセージ
main.cpp:48:9: warning: #pragma once in main file
48 | #pragma once
| ^~~~
main.cpp:101:9: warning: #pragma once in main file
101 | #pragma once
| ^~~~
main.cpp:113:9: warning: #pragma once in main file
113 | #pragma once
| ^~~~
ソースコード
// https://x.com/akakimidori/status/1610658801933496323
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
template<class T>bool chmax(T &a, const T &b) { if (a<b) { a=b; return true; } return false; }
template<class T>bool chmin(T &a, const T &b) { if (b<a) { a=b; return true; } return false; }
#define vi vector<int>
#define vl vector<ll>
#define vii vector<pair<int,int>>
#define vll vector<pair<ll,ll>>
#define vvi vector<vector<int>>
#define vvl vector<vector<ll>>
#define vvii vector<vector<pair<int,int>>>
#define vvll vector<vector<pair<ll,ll>>>
#define vst vector<string>
#define pii pair<int,int>
#define pll pair<ll,ll>
#define pb push_back
#define all(x) (x).begin(),(x).end()
#define mkunique(x) sort(all(x));(x).erase(unique(all(x)),(x).end())
#define fi first
#define se second
#define mp make_pair
#define si(x) int(x.size())
const int mod=998244353,MAX=200005,INF=15<<26;
#pragma GCC optimize("O3,unroll-loops")
#pragma GCC target("avx2,bmi,bmi2,lzcnt,popcnt")
//高速素因数分解
/**
* Author: chilli, Ramchandra Apte, Noam527, Simon Lindholm
* Date: 2019-04-24
* License: CC0
* Source: https://github.com/RamchandraApte/OmniTemplate/blob/master/modulo.hpp…
* Description: Calculate $a\cdot b\bmod c$ (or $a^b \bmod c$) for $0 \le a, b \le c \le 7.2\cdot 10^{18}$.
* Time: O(1) for \texttt{modmul}, O(\log b) for \texttt{modpow}
* Status: stress-tested, proven correct
* Details:
* This runs ~2x faster than the naive (__int128_t)a * b % M.
* A proof of correctness is in doc/modmul-proof.tex. An earlier version of the proof,
* from when the code used a * b / (long double)M, is in doc/modmul-proof.md.
* The proof assumes that long doubles are implemented as x87 80-bit floats; if they
* are 64-bit, as on e.g. MSVC, the implementation is only valid for
* $0 \le a, b \le c < 2^{52} \approx 4.5 \cdot 10^{15}$.
*/
#pragma once
typedef unsigned long long ull;
ull modmul(ull a, ull b, ull M) {
ll ret = a * b - M * ull(1.L / M * a * b);
return ret + M * (ret < 0) - M * (ret >= (ll)M);
}
ull modpow(ull b, ull e, ull mod) {
ull ans = 1;
for (; e; b = modmul(b, b, mod), e /= 2)
if (e & 1) ans = modmul(ans, b, mod);
return ans;
}
/**
* Author: chilli, SJTU, pajenegod
* Date: 2020-03-04
* License: CC0
* Source: own
* Description: Pollard-rho randomized factorization algorithm. Returns prime
* factors of a number, in arbitrary order (e.g. 2299 -> \{11, 19, 11\}).
* Time: $O(n^{1/4})$, less for numbers with small factors.
* Status: stress-tested
*
* Details: This implementation uses the improvement described here
* (https://en.wikipedia.org/wiki/Pollard%27s_rho_algorithm#Variants…), where
* one can accumulate gcd calls by some factor (40 chosen here through
* exhaustive testing). This improves performance by approximately 6-10x
* depending on the inputs and speed of gcd. Benchmark found here:
* (https://ideone.com/nGGD9T)
*
* GCD can be improved by a factor of 1.75x using Binary GCD
* (https://lemire.me/blog/2013/12/26/fastest-way-to-compute-the-greatest-common-divisor/…).
* However, with the gcd accumulation the bottleneck moves from the gcd calls
* to the modmul. As GCD only constitutes ~12% of runtime, speeding it up
* doesn't matter so much.
*
* This code can probably be sped up by using a faster mod mul - potentially
* montgomery reduction on 128 bit integers.
* Alternatively, one can use a quadratic sieve for an asymptotic improvement,
* which starts being faster in practice around 1e13.
*
* Brent's cycle finding algorithm was tested, but doesn't reduce modmul calls
* significantly.
*
* Subtle implementation notes:
* - we operate on residues in [1, n]; modmul can be proven to work for those
* - prd starts off as 2 to handle the case n = 4; it's harmless for other n
* since we're guaranteed that n > 2. (Pollard rho has problems with prime
* powers in general, but all larger ones happen to work.)
* - t starts off as 30 to make the first gcd check come earlier, as an
* optimization for small numbers.
*/
#pragma once
/**
* Author: chilli, c1729, Simon Lindholm
* Date: 2019-03-28
* License: CC0
* Source: Wikipedia, https://miller-rabin.appspot.com
* Description: Deterministic Miller-Rabin primality test.
* Guaranteed to work for numbers up to $7 \cdot 10^{18}$; for larger numbers, use Python and extend A randomly.
* Time: 7 times the complexity of $a^b \mod c$.
* Status: Stress-tested
*/
#pragma once
bool isPrime(ull n) {
if (n < 2 || n % 6 % 4 != 1) return (n | 1) == 3;
ull A[] = {2, 325, 9375, 28178, 450775, 9780504, 1795265022},
s = __builtin_ctzll(n-1), d = n >> s;
for (ull a : A) { // ^ count trailing zeroes
ull p = modpow(a%n, d, n), i = s;
while (p != 1 && p != n - 1 && a % n && i--)
p = modmul(p, p, n);
if (p != n-1 && i != s) return 0;
}
return 1;
}
ull pollard(ull n) {
auto f = [n](ull x) { return modmul(x, x, n) + 1; };
ull x = 0, y = 0, t = 30, prd = 2, i = 1, q;
while (t++ % 40 || __gcd(prd, n) == 1) {
if (x == y) x = ++i, y = f(x);
if ((q = modmul(prd, max(x,y) - min(x,y), n))) prd = q;
x = f(x), y = f(f(y));
}
return __gcd(prd, n);
}
vector<ull> factor(ull n) {
if (n == 1) return {};
if (isPrime(n)) return {n};
ull x = pollard(n);
auto l = factor(x), r = factor(n / x);
l.insert(l.end(), all(r));
return l;
}
vector<int> prime;//i番目の素数
bool is_prime[MAX+1];
vi fac[MAX+1];
int pp[MAX+1];
void sieve(int n){
for(int i=0;i<=n;i++){
is_prime[i]=true;
}
is_prime[0]=is_prime[1]=false;
for(int i=2;i<=n;i++){
if(is_prime[i]){
prime.push_back(i);
fac[i].pb(i);
ll z=i;
while(z<=n){
pp[z]=i;
z*=i;
}
for(int j=2*i;j<=n;j+=i){
is_prime[j] = false;
int now=j,k=1;
while(now%i==0){
k*=i;
now/=i;
fac[j].pb(k);
}
}
}
}
}
//modint+畳み込み+逆元テーブル
// from: https://gist.github.com/yosupo06/ddd51afb727600fd95d9d8ad6c3c80c9
// (based on AtCoder STL)
#include <algorithm>
#include <array>
#ifdef _MSC_VER
#include <intrin.h>
#endif
namespace atcoder {
namespace internal {
int ceil_pow2(int n) {
int x = 0;
while ((1U << x) < (unsigned int)(n)) x++;
return x;
}
int bsf(unsigned int n) {
#ifdef _MSC_VER
unsigned long index;
_BitScanForward(&index, n);
return index;
#else
return __builtin_ctz(n);
#endif
}
} // namespace internal
} // namespace atcoder
#include <utility>
namespace atcoder {
namespace internal {
constexpr long long safe_mod(long long x, long long m) {
x %= m;
if (x < 0) x += m;
return x;
}
struct barrett {
unsigned int _m;
unsigned long long im;
barrett(unsigned int m) : _m(m), im((unsigned long long)(-1) / m + 1) {}
unsigned int umod() const { return _m; }
unsigned int mul(unsigned int a, unsigned int b) const {
unsigned long long z = a;
z *= b;
#ifdef _MSC_VER
unsigned long long x;
_umul128(z, im, &x);
#else
unsigned long long x =
(unsigned long long)(((unsigned __int128)(z)*im) >> 64);
#endif
unsigned int v = (unsigned int)(z - x * _m);
if (_m <= v) v += _m;
return v;
}
};
constexpr long long pow_mod_constexpr(long long x, long long n, int m) {
if (m == 1) return 0;
unsigned int _m = (unsigned int)(m);
unsigned long long r = 1;
unsigned long long y = safe_mod(x, m);
while (n) {
if (n & 1) r = (r * y) % _m;
y = (y * y) % _m;
n >>= 1;
}
return r;
}
constexpr bool is_prime_constexpr(int n) {
if (n <= 1) return false;
if (n == 2 || n == 7 || n == 61) return true;
if (n % 2 == 0) return false;
long long d = n - 1;
while (d % 2 == 0) d /= 2;
for (long long a : {2, 7, 61}) {
long long t = d;
long long y = pow_mod_constexpr(a, t, n);
while (t != n - 1 && y != 1 && y != n - 1) {
y = y * y % n;
t <<= 1;
}
if (y != n - 1 && t % 2 == 0) {
return false;
}
}
return true;
}
template <int n> constexpr bool is_prime = is_prime_constexpr(n);
constexpr std::pair<long long, long long> inv_gcd(long long a, long long b) {
a = safe_mod(a, b);
if (a == 0) return {b, 0};
long long s = b, t = a;
long long m0 = 0, m1 = 1;
while (t) {
long long u = s / t;
s -= t * u;
m0 -= m1 * u; // |m1 * u| <= |m1| * s <= b
auto tmp = s;
s = t;
t = tmp;
tmp = m0;
m0 = m1;
m1 = tmp;
}
if (m0 < 0) m0 += b / s;
return {s, m0};
}
constexpr int primitive_root_constexpr(int m) {
if (m == 2) return 1;
if (m == 167772161) return 3;
if (m == 469762049) return 3;
if (m == 754974721) return 11;
if (m == 998244353) return 3;
int divs[20] = {};
divs[0] = 2;
int cnt = 1;
int x = (m - 1) / 2;
while (x % 2 == 0) x /= 2;
for (int i = 3; (long long)(i)*i <= x; i += 2) {
if (x % i == 0) {
divs[cnt++] = i;
while (x % i == 0) {
x /= i;
}
}
}
if (x > 1) {
divs[cnt++] = x;
}
for (int g = 2;; g++) {
bool ok = true;
for (int i = 0; i < cnt; i++) {
if (pow_mod_constexpr(g, (m - 1) / divs[i], m) == 1) {
ok = false;
break;
}
}
if (ok) return g;
}
}
template <int m> constexpr int primitive_root = primitive_root_constexpr(m);
} // namespace internal
} // namespace atcoder
#include <cassert>
#include <numeric>
#include <type_traits>
namespace atcoder {
namespace internal {
#ifndef _MSC_VER
template <class T>
using is_signed_int128 =
typename std::conditional<std::is_same<T, __int128_t>::value ||
std::is_same<T, __int128>::value,
std::true_type,
std::false_type>::type;
template <class T>
using is_unsigned_int128 =
typename std::conditional<std::is_same<T, __uint128_t>::value ||
std::is_same<T, unsigned __int128>::value,
std::true_type,
std::false_type>::type;
template <class T>
using make_unsigned_int128 =
typename std::conditional<std::is_same<T, __int128_t>::value,
__uint128_t,
unsigned __int128>;
template <class T>
using is_integral = typename std::conditional<std::is_integral<T>::value ||
is_signed_int128<T>::value ||
is_unsigned_int128<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using is_signed_int = typename std::conditional<(is_integral<T>::value &&
std::is_signed<T>::value) ||
is_signed_int128<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using is_unsigned_int =
typename std::conditional<(is_integral<T>::value &&
std::is_unsigned<T>::value) ||
is_unsigned_int128<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using to_unsigned = typename std::conditional<
is_signed_int128<T>::value,
make_unsigned_int128<T>,
typename std::conditional<std::is_signed<T>::value,
std::make_unsigned<T>,
std::common_type<T>>::type>::type;
#else
template <class T> using is_integral = typename std::is_integral<T>;
template <class T>
using is_signed_int =
typename std::conditional<is_integral<T>::value && std::is_signed<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using is_unsigned_int =
typename std::conditional<is_integral<T>::value &&
std::is_unsigned<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using to_unsigned = typename std::conditional<is_signed_int<T>::value,
std::make_unsigned<T>,
std::common_type<T>>::type;
#endif
template <class T>
using is_signed_int_t = std::enable_if_t<is_signed_int<T>::value>;
template <class T>
using is_unsigned_int_t = std::enable_if_t<is_unsigned_int<T>::value>;
template <class T> using to_unsigned_t = typename to_unsigned<T>::type;
} // namespace internal
} // namespace atcoder
#include <cassert>
#include <numeric>
#include <type_traits>
#ifdef _MSC_VER
#include <intrin.h>
#endif
namespace atcoder {
namespace internal {
struct modint_base {};
struct static_modint_base : modint_base {};
template <class T> using is_modint = std::is_base_of<modint_base, T>;
template <class T> using is_modint_t = std::enable_if_t<is_modint<T>::value>;
} // namespace internal
template <int m, std::enable_if_t<(1 <= m)>* = nullptr>
struct static_modint : internal::static_modint_base {
using mint = static_modint;
public:
static constexpr int mod() { return m; }
static mint raw(int v) {
mint x;
x._v = v;
return x;
}
static_modint() : _v(0) {}
template <class T, internal::is_signed_int_t<T>* = nullptr>
static_modint(T v) {
long long x = (long long)(v % (long long)(umod()));
if (x < 0) x += umod();
_v = (unsigned int)(x);
}
template <class T, internal::is_unsigned_int_t<T>* = nullptr>
static_modint(T v) {
_v = (unsigned int)(v % umod());
}
static_modint(bool v) { _v = ((unsigned int)(v) % umod()); }
unsigned int val() const { return _v; }
mint& operator++() {
_v++;
if (_v == umod()) _v = 0;
return *this;
}
mint& operator--() {
if (_v == 0) _v = umod();
_v--;
return *this;
}
mint operator++(int) {
mint result = *this;
++*this;
return result;
}
mint operator--(int) {
mint result = *this;
--*this;
return result;
}
mint& operator+=(const mint& rhs) {
_v += rhs._v;
if (_v >= umod()) _v -= umod();
return *this;
}
mint& operator-=(const mint& rhs) {
_v -= rhs._v;
if (_v >= umod()) _v += umod();
return *this;
}
mint& operator*=(const mint& rhs) {
unsigned long long z = _v;
z *= rhs._v;
_v = (unsigned int)(z % umod());
return *this;
}
mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }
mint operator+() const { return *this; }
mint operator-() const { return mint() - *this; }
mint pow(long long n) const {
assert(0 <= n);
mint x = *this, r = 1;
while (n) {
if (n & 1) r *= x;
x *= x;
n >>= 1;
}
return r;
}
mint inv() const {
if (prime) {
assert(_v);
return pow(umod() - 2);
} else {
auto eg = internal::inv_gcd(_v, m);
assert(eg.first == 1);
return eg.second;
}
}
friend mint operator+(const mint& lhs, const mint& rhs) {
return mint(lhs) += rhs;
}
friend mint operator-(const mint& lhs, const mint& rhs) {
return mint(lhs) -= rhs;
}
friend mint operator*(const mint& lhs, const mint& rhs) {
return mint(lhs) *= rhs;
}
friend mint operator/(const mint& lhs, const mint& rhs) {
return mint(lhs) /= rhs;
}
friend bool operator==(const mint& lhs, const mint& rhs) {
return lhs._v == rhs._v;
}
friend bool operator!=(const mint& lhs, const mint& rhs) {
return lhs._v != rhs._v;
}
private:
unsigned int _v;
static constexpr unsigned int umod() { return m; }
static constexpr bool prime = internal::is_prime<m>;
};
template <int id> struct dynamic_modint : internal::modint_base {
using mint = dynamic_modint;
public:
static int mod() { return (int)(bt.umod()); }
static void set_mod(int m) {
assert(1 <= m);
bt = internal::barrett(m);
}
static mint raw(int v) {
mint x;
x._v = v;
return x;
}
dynamic_modint() : _v(0) {}
template <class T, internal::is_signed_int_t<T>* = nullptr>
dynamic_modint(T v) {
long long x = (long long)(v % (long long)(mod()));
if (x < 0) x += mod();
_v = (unsigned int)(x);
}
template <class T, internal::is_unsigned_int_t<T>* = nullptr>
dynamic_modint(T v) {
_v = (unsigned int)(v % mod());
}
dynamic_modint(bool v) { _v = ((unsigned int)(v) % mod()); }
unsigned int val() const { return _v; }
mint& operator++() {
_v++;
if (_v == umod()) _v = 0;
return *this;
}
mint& operator--() {
if (_v == 0) _v = umod();
_v--;
return *this;
}
mint operator++(int) {
mint result = *this;
++*this;
return result;
}
mint operator--(int) {
mint result = *this;
--*this;
return result;
}
mint& operator+=(const mint& rhs) {
_v += rhs._v;
if (_v >= umod()) _v -= umod();
return *this;
}
mint& operator-=(const mint& rhs) {
_v += mod() - rhs._v;
if (_v >= umod()) _v -= umod();
return *this;
}
mint& operator*=(const mint& rhs) {
_v = bt.mul(_v, rhs._v);
return *this;
}
mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }
mint operator+() const { return *this; }
mint operator-() const { return mint() - *this; }
mint pow(long long n) const {
assert(0 <= n);
mint x = *this, r = 1;
while (n) {
if (n & 1) r *= x;
x *= x;
n >>= 1;
}
return r;
}
mint inv() const {
auto eg = internal::inv_gcd(_v, mod());
assert(eg.first == 1);
return eg.second;
}
friend mint operator+(const mint& lhs, const mint& rhs) {
return mint(lhs) += rhs;
}
friend mint operator-(const mint& lhs, const mint& rhs) {
return mint(lhs) -= rhs;
}
friend mint operator*(const mint& lhs, const mint& rhs) {
return mint(lhs) *= rhs;
}
friend mint operator/(const mint& lhs, const mint& rhs) {
return mint(lhs) /= rhs;
}
friend bool operator==(const mint& lhs, const mint& rhs) {
return lhs._v == rhs._v;
}
friend bool operator!=(const mint& lhs, const mint& rhs) {
return lhs._v != rhs._v;
}
private:
unsigned int _v;
static internal::barrett bt;
static unsigned int umod() { return bt.umod(); }
};
template <int id> internal::barrett dynamic_modint<id>::bt = 998244353;
using modint998244353 = static_modint<998244353>;
using modint1000000007 = static_modint<1000000007>;
using modint = dynamic_modint<-1>;
namespace internal {
template <class T>
using is_static_modint = std::is_base_of<internal::static_modint_base, T>;
template <class T>
using is_static_modint_t = std::enable_if_t<is_static_modint<T>::value>;
template <class> struct is_dynamic_modint : public std::false_type {};
template <int id>
struct is_dynamic_modint<dynamic_modint<id>> : public std::true_type {};
template <class T>
using is_dynamic_modint_t = std::enable_if_t<is_dynamic_modint<T>::value>;
} // namespace internal
} // namespace atcoder
#include <cassert>
#include <type_traits>
#include <vector>
namespace atcoder {
namespace internal {
template <class mint, internal::is_static_modint_t<mint>* = nullptr>
void butterfly(std::vector<mint>& a) {
static constexpr int g = internal::primitive_root<mint::mod()>;
int n = int(a.size());
int h = internal::ceil_pow2(n);
static bool first = true;
static mint sum_e[30]; // sum_e[i] = ies[0] * ... * ies[i - 1] * es[i]
if (first) {
first = false;
mint es[30], ies[30]; // es[i]^(2^(2+i)) == 1
int cnt2 = bsf(mint::mod() - 1);
mint e = mint(g).pow((mint::mod() - 1) >> cnt2), ie = e.inv();
for (int i = cnt2; i >= 2; i--) {
es[i - 2] = e;
ies[i - 2] = ie;
e *= e;
ie *= ie;
}
mint now = 1;
for (int i = 0; i < cnt2 - 2; i++) {
sum_e[i] = es[i] * now;
now *= ies[i];
}
}
for (int ph = 1; ph <= h; ph++) {
int w = 1 << (ph - 1), p = 1 << (h - ph);
mint now = 1;
for (int s = 0; s < w; s++) {
int offset = s << (h - ph + 1);
for (int i = 0; i < p; i++) {
auto l = a[i + offset];
auto r = a[i + offset + p] * now;
a[i + offset] = l + r;
a[i + offset + p] = l - r;
}
now *= sum_e[bsf(~(unsigned int)(s))];
}
}
}
template <class mint, internal::is_static_modint_t<mint>* = nullptr>
void butterfly_inv(std::vector<mint>& a) {
static constexpr int g = internal::primitive_root<mint::mod()>;
int n = int(a.size());
int h = internal::ceil_pow2(n);
static bool first = true;
static mint sum_ie[30]; // sum_ie[i] = es[0] * ... * es[i - 1] * ies[i]
if (first) {
first = false;
mint es[30], ies[30]; // es[i]^(2^(2+i)) == 1
int cnt2 = bsf(mint::mod() - 1);
mint e = mint(g).pow((mint::mod() - 1) >> cnt2), ie = e.inv();
for (int i = cnt2; i >= 2; i--) {
es[i - 2] = e;
ies[i - 2] = ie;
e *= e;
ie *= ie;
}
mint now = 1;
for (int i = 0; i < cnt2 - 2; i++) {
sum_ie[i] = ies[i] * now;
now *= es[i];
}
}
for (int ph = h; ph >= 1; ph--) {
int w = 1 << (ph - 1), p = 1 << (h - ph);
mint inow = 1;
for (int s = 0; s < w; s++) {
int offset = s << (h - ph + 1);
for (int i = 0; i < p; i++) {
auto l = a[i + offset];
auto r = a[i + offset + p];
a[i + offset] = l + r;
a[i + offset + p] =
(unsigned long long)(mint::mod() + l.val() - r.val()) *
inow.val();
}
inow *= sum_ie[bsf(~(unsigned int)(s))];
}
}
}
} // namespace internal
template <class mint, internal::is_static_modint_t<mint>* = nullptr>
std::vector<mint> convolution(std::vector<mint> a, std::vector<mint> b) {
int n = int(a.size()), m = int(b.size());
if (!n || !m) return {};
if (std::min(n, m) <= 60) {
if (n < m) {
std::swap(n, m);
std::swap(a, b);
}
std::vector<mint> ans(n + m - 1);
for (int i = 0; i < n; i++) {
for (int j = 0; j < m; j++) {
ans[i + j] += a[i] * b[j];
}
}
return ans;
}
int z = 1 << internal::ceil_pow2(n + m - 1);
a.resize(z);
internal::butterfly(a);
b.resize(z);
internal::butterfly(b);
for (int i = 0; i < z; i++) {
a[i] *= b[i];
}
internal::butterfly_inv(a);
a.resize(n + m - 1);
mint iz = mint(z).inv();
for (int i = 0; i < n + m - 1; i++) a[i] *= iz;
return a;
}
template <unsigned int mod = 998244353,
class T,
std::enable_if_t<internal::is_integral<T>::value>* = nullptr>
std::vector<T> convolution(const std::vector<T>& a, const std::vector<T>& b) {
int n = int(a.size()), m = int(b.size());
if (!n || !m) return {};
using mint = static_modint<mod>;
std::vector<mint> a2(n), b2(m);
for (int i = 0; i < n; i++) {
a2[i] = mint(a[i]);
}
for (int i = 0; i < m; i++) {
b2[i] = mint(b[i]);
}
auto c2 = convolution(move(a2), move(b2));
std::vector<T> c(n + m - 1);
for (int i = 0; i < n + m - 1; i++) {
c[i] = c2[i].val();
}
return c;
}
std::vector<long long> convolution_ll(const std::vector<long long>& a,
const std::vector<long long>& b) {
int n = int(a.size()), m = int(b.size());
if (!n || !m) return {};
static constexpr unsigned long long MOD1 = 754974721; // 2^24
static constexpr unsigned long long MOD2 = 167772161; // 2^25
static constexpr unsigned long long MOD3 = 469762049; // 2^26
static constexpr unsigned long long M2M3 = MOD2 * MOD3;
static constexpr unsigned long long M1M3 = MOD1 * MOD3;
static constexpr unsigned long long M1M2 = MOD1 * MOD2;
static constexpr unsigned long long M1M2M3 = MOD1 * MOD2 * MOD3;
static constexpr unsigned long long i1 =
internal::inv_gcd(MOD2 * MOD3, MOD1).second;
static constexpr unsigned long long i2 =
internal::inv_gcd(MOD1 * MOD3, MOD2).second;
static constexpr unsigned long long i3 =
internal::inv_gcd(MOD1 * MOD2, MOD3).second;
auto c1 = convolution<MOD1>(a, b);
auto c2 = convolution<MOD2>(a, b);
auto c3 = convolution<MOD3>(a, b);
std::vector<long long> c(n + m - 1);
for (int i = 0; i < n + m - 1; i++) {
unsigned long long x = 0;
x += (c1[i] * i1) % MOD1 * M2M3;
x += (c2[i] * i2) % MOD2 * M1M3;
x += (c3[i] * i3) % MOD3 * M1M2;
long long diff =
c1[i] - internal::safe_mod((long long)(x), (long long)(MOD1));
if (diff < 0) diff += MOD1;
static constexpr unsigned long long offset[5] = {
0, 0, M1M2M3, 2 * M1M2M3, 3 * M1M2M3};
x -= offset[diff % 5];
c[i] = x;
}
return c;
}
} // namespace atcoder
using mint=atcoder::modint998244353;
//2d point update rectangle sum
// https://kopricky.github.io/code/SegmentTrees/rangetree_pointupdate.html
template<typename T> class segtree {
private:
int n, sz;
vector<T> node;
public:
void init(const vector<T>& v){
sz = (int)v.size();
n = 1;
while(n < sz){
n *= 2;
}
node.assign(2*n, 1);
for(int i = 0; i < sz; i++){
node[i+n] = v[i];
}
for(int i=n-1; i>=1; i--){
node[i] = node[2*i] * node[2*i+1];
}
}
void update(int k, const T a)
{
node[k+=n] *= a;
while(k>>=1){
node[k] = node[2*k] * node[2*k+1];
}
}
T query(int a, int b)
{
T res1 = 1, res2 = 1;
a += n, b += n;
while(a != b){
if(a % 2) res1 = res1 * node[a++];
if(b % 2) res2 = res2 * node[--b];
a >>= 1, b >>= 1;
}
return res1 * res2;
}
void print(){
for(int i = 0; i < sz; i++){
cout << query(i, i+1) << " ";
}
cout << endl;
}
};
//座標の型, 値の型
template<typename CandidateType, typename ValueType> class RangeTree
{
public:
static_assert(std::is_integral<CandidateType>::value, "Integral required.");
private:
using CT = CandidateType;
using VT = ValueType;
using pcc = pair<CT, CT>;
using pci = pair<CT, int>;
int n, sz;
vector<segtree<VT> > seg;
// y座標, x座標
vector<vector<pcc> > yx;
// y座標, x座標
vector<pcc> sorted;
void update_(int id, const CT x, const CT y, const VT val) {
id += n-1;
const int yid = lower_bound(all(yx[id]), pcc(y, x)) - yx[id].begin();
seg[id].update(yid, val);
while(id > 0){
id = (id - 1) / 2;
const int yid = lower_bound(all(yx[id]), pcc(y, x)) - yx[id].begin();
seg[id].update(yid, val);
}
}
VT query(const int lxid, const int rxid, const CT ly, const CT ry, const int k, const int l, const int r) {
if(r <= lxid || rxid <= l) return 1;
if(lxid <= l && r <= rxid){
const int lyid = lower_bound(all(yx[k]), pcc(ly, numeric_limits<CT>::min())) - yx[k].begin();
const int ryid = upper_bound(all(yx[k]), pcc(ry, numeric_limits<CT>::min())) - yx[k].begin();
return (lyid >= ryid) ? 1 : seg[k].query(lyid, ryid);
}else{
return query(lxid, rxid, ly, ry, 2*k+1, l, (l+r)/2) * query(lxid, rxid, ly, ry, 2*k+2, (l+r)/2, r) ;
}
}
public:
// 座標, 点の値
RangeTree(const vector<pcc>& cand, const vector<VT>& val) : n(1), sz((int)cand.size()), sorted(sz){
while(n < sz) n *= 2;
for(int i = 0; i < sz; ++i){
sorted[i] = {cand[i].first, i};
}
sort(all(sorted), [&](const pcc& a, const pcc& b){
return (a.first == b.first) ? (cand[a.second].second < cand[b.second].second) : (a.first < b.first);
});
yx.resize(2*n-1), seg.resize(2*n-1);
for(int i = 0; i < sz; ++i){
yx[i+n-1] = {{sorted[i].second, sorted[i].first}};
vector<VT> arg = {val[sorted[i].second]};
seg[i+n-1].init(arg);
sorted[i].second = cand[sorted[i].second].second;
}
for(int i = n-2; i >= 0; --i){
yx[i].resize((int)yx[2*i+1].size() + (int)yx[2*i+2].size());
if(yx[i].empty()) continue;
merge(all(yx[2*i+1]), all(yx[2*i+2]), yx[i].begin(), [&](const pcc& a, const pcc& b){
return (cand[a.first].second == cand[b.first].second)
? (a.second < b.second) : (cand[a.first].second < cand[b.first].second);
});
vector<VT> arg((int)yx[i].size());
for(int j = 0; j < (int)yx[i].size(); ++j){
arg[j] = val[yx[i][j].first];
}
seg[i].init(arg);
}
for(int i = 0; i < 2*n-1; ++i){
for(pcc& e : yx[i]){
e.first = cand[e.first].second;
}
}
}
// 点 (x,y) の更新を行う
void update(const CT x, const CT y, const VT val){
const int id = lower_bound(all(sorted), pcc(x, y)) - sorted.begin();
return update_(id, x, y, val);
}
// [lx,rx) × [ly,ry) の長方形領域のクエリに答える
VT query(const CT lx, const CT ly, const CT rx, const CT ry){
const int lxid = lower_bound(all(sorted), pcc(lx, numeric_limits<CT>::min())) - sorted.begin();
const int rxid = upper_bound(all(sorted), pcc(rx, numeric_limits<CT>::min())) - sorted.begin();
return (lxid >= rxid) ? 1 : query(lxid, rxid, ly, ry, 0, 0, n);
}
};
vi po[MAX];
int main(){
std::ifstream in("text.txt");
std::cin.rdbuf(in.rdbuf());
cin.tie(0);
ios::sync_with_stdio(false);
sieve(200000);
ll N;cin>>N;
vl A(N);
for(int i=0;i<N;i++){
cin>>A[i];
for(int p:fac[A[i]]){
po[p].pb(i);
//cout<<p<<" "<<i<<endl;
}
}
vii S;
vector<mint> T;
for(int i=1;i<=200000;i++){
for(int j=0;j<si(po[i]);j++){
S.pb(mp(po[i][j],po[i][j]));
if(j) S.pb(mp(po[i][j-1],po[i][j]));
}
}
mkunique(S);
T.assign(si(S),1);
for(int i=1;i<=200000;i++){
for(int j=0;j<si(po[i]);j++){
{
int s=lower_bound(all(S),mp(po[i][j],po[i][j]))-S.begin();
T[s]*=pp[i];
}
if(j){
int s=lower_bound(all(S),mp(po[i][j-1],po[i][j]))-S.begin();
T[s]/=pp[i];
}
//cout<<i<<" "<<pp[i]<<endl;
}
}
for(int i=0;i<si(S);i++){
//cout<<S[i].fi<<" "<<S[i].se<<" "<<T[i].val()<<endl;
}
RangeTree<int,mint> RT(S,T);
int Q;cin>>Q;
ll la=1;
while(Q--){
ll a,b;cin>>a>>b;
ll x=(la*a)%mod;
ll y=x%N+1;
ll z=(b*la)%mod;
ll w=z%N+1;
ll l=min(y,w);
ll r=max(y,w);
l--;
//cout<<l<<" "<<r<<endl;
ll ans=RT.query(l,l,r,r).val();
cout<<ans<<"\n";
la=ans;
}
}