結果
問題 | No.1931 Fraction 2 |
ユーザー |
![]() |
提出日時 | 2022-05-06 22:29:23 |
言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 256 ms / 2,000 ms |
コード長 | 23,181 bytes |
コンパイル時間 | 3,046 ms |
コンパイル使用メモリ | 227,696 KB |
最終ジャッジ日時 | 2025-01-29 03:45:42 |
ジャッジサーバーID (参考情報) |
judge1 / judge3 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 3 |
other | AC * 36 |
ソースコード
#line 1 "/home/maspy/compro/library/my_template.hpp"#include <bits/stdc++.h>using namespace std;using ll = long long;using pi = pair<ll, ll>;using vi = vector<ll>;using u32 = unsigned int;using u64 = unsigned long long;using i128 = __int128;template <class T>using vc = vector<T>;template <class T>using vvc = vector<vc<T>>;template <class T>using vvvc = vector<vvc<T>>;template <class T>using vvvvc = vector<vvvc<T>>;template <class T>using vvvvvc = vector<vvvvc<T>>;template <class T>using pq = priority_queue<T>;template <class T>using pqg = priority_queue<T, vector<T>, greater<T>>;#define vec(type, name, ...) vector<type> name(__VA_ARGS__)#define vv(type, name, h, ...) \vector<vector<type>> name(h, vector<type>(__VA_ARGS__))#define vvv(type, name, h, w, ...) \vector<vector<vector<type>>> name( \h, vector<vector<type>>(w, vector<type>(__VA_ARGS__)))#define vvvv(type, name, a, b, c, ...) \vector<vector<vector<vector<type>>>> name( \a, vector<vector<vector<type>>>( \b, vector<vector<type>>(c, vector<type>(__VA_ARGS__))))#define FOR_(n) for (ll _ = 0; (_) < (ll)(n); ++(_))#define FOR(i, n) for (ll i = 0; (i) < (ll)(n); ++(i))#define FOR3(i, m, n) for (ll i = (m); (i) < (ll)(n); ++(i))#define FOR_R(i, n) for (ll i = (ll)(n)-1; (i) >= 0; --(i))#define FOR3_R(i, m, n) for (ll i = (ll)(n)-1; (i) >= (ll)(m); --(i))#define FOR_subset(t, s) for (ll t = s; t >= 0; t = (t == 0 ? -1 : (t - 1) & s))#define all(x) x.begin(), x.end()#define len(x) ll(x.size())#define elif else if#define eb emplace_back#define mp make_pair#define mt make_tuple#define fi first#define se second#define stoi stolltemplate <typename T>T SUM(vector<T> &A) {T sum = T(0);for (auto &&a: A) sum += a;return sum;}#define MIN(v) *min_element(all(v))#define MAX(v) *max_element(all(v))#define LB(c, x) distance((c).begin(), lower_bound(all(c), (x)))#define UB(c, x) distance((c).begin(), upper_bound(all(c), (x)))#define UNIQUE(x) sort(all(x)), x.erase(unique(all(x)), x.end())int popcnt(int x) { return __builtin_popcount(x); }int popcnt(u32 x) { return __builtin_popcount(x); }int popcnt(ll x) { return __builtin_popcountll(x); }int popcnt(u64 x) { return __builtin_popcountll(x); }// (0, 1, 2, 3, 4) -> (-1, 0, 1, 1, 2)int topbit(int x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }int topbit(u32 x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }int topbit(ll x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }int topbit(u64 x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }// (0, 1, 2, 3, 4) -> (-1, 0, 1, 0, 2)int lowbit(int x) { return (x == 0 ? -1 : __builtin_ctz(x)); }int lowbit(u32 x) { return (x == 0 ? -1 : __builtin_ctz(x)); }int lowbit(ll x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }int lowbit(u64 x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }template <typename T, typename U>T ceil(T x, U y) {return (x > 0 ? (x + y - 1) / y : x / y);}template <typename T, typename U>T floor(T x, U y) {return (x > 0 ? x / y : (x - y + 1) / y);}template <typename T, typename U>pair<T, T> divmod(T x, U y) {T q = floor(x, y);return {q, x - q * y};}ll binary_search(function<bool(ll)> check, ll ok, ll ng) {assert(check(ok));while (abs(ok - ng) > 1) {auto x = (ng + ok) / 2;if (check(x))ok = x;elseng = x;}return ok;}template <class T, class S>inline bool chmax(T &a, const S &b) {return (a < b ? a = b, 1 : 0);}template <class T, class S>inline bool chmin(T &a, const S &b) {return (a > b ? a = b, 1 : 0);}vi s_to_vi(const string& S, char first_char) {vi A(S.size());FOR(i, S.size()) { A[i] = S[i] - first_char; }return A;}template <typename T>vector<T> cumsum(vector<T> &A, int off = 1) {int N = A.size();vector<T> B(N + 1);FOR(i, N) { B[i + 1] = B[i] + A[i]; }if (off == 0) B.erase(B.begin());return B;}template <typename CNT, typename T>vc<CNT> bincount(const vc<T> &A, int size) {vc<CNT> C(size);for (auto &&x: A) { ++C[x]; }return C;}template <typename T>vector<int> argsort(const vector<T> &A) {// stablevector<int> ids(A.size());iota(all(ids), 0);sort(all(ids),[&](int i, int j) { return A[i] < A[j] || (A[i] == A[j] && i < j); });return ids;}// A[I[0]], A[I[1]], ...template <typename T>vc<T> rearrange(const vc<T> &A, const vc<int> &I) {int n = len(A);assert(len(I) == n);vc<T> B(n);FOR(i, n) B[i] = A[I[i]];return B;}#line 1 "/home/maspy/compro/library/other/io.hpp"// based on yosupo's fastio#include <unistd.h>namespace detail {template <typename T, decltype(&T::is_modint) = &T::is_modint>std::true_type check_value(int);template <typename T>std::false_type check_value(long);} // namespace detailtemplate <typename T>struct is_modint : decltype(detail::check_value<T>(0)) {};template <typename T>using is_modint_t = enable_if_t<is_modint<T>::value>;template <typename T>using is_not_modint_t = enable_if_t<!is_modint<T>::value>;struct Scanner {FILE *fp;char line[(1 << 15) + 1];size_t st = 0, ed = 0;void reread() {memmove(line, line + st, ed - st);ed -= st;st = 0;ed += fread(line + ed, 1, (1 << 15) - ed, fp);line[ed] = '\0';}bool succ() {while (true) {if (st == ed) {reread();if (st == ed) return false;}while (st != ed && isspace(line[st])) st++;if (st != ed) break;}if (ed - st <= 50) {bool sep = false;for (size_t i = st; i < ed; i++) {if (isspace(line[i])) {sep = true;break;}}if (!sep) reread();}return true;}template <class T, enable_if_t<is_same<T, string>::value, int> = 0>bool read_single(T &ref) {if (!succ()) return false;while (true) {size_t sz = 0;while (st + sz < ed && !isspace(line[st + sz])) sz++;ref.append(line + st, sz);st += sz;if (!sz || st != ed) break;reread();}return true;}template <class T, enable_if_t<is_integral<T>::value, int> = 0>bool read_single(T &ref) {if (!succ()) return false;bool neg = false;if (line[st] == '-') {neg = true;st++;}ref = T(0);while (isdigit(line[st])) { ref = 10 * ref + (line[st++] & 0xf); }if (neg) ref = -ref;return true;}template <class T, is_modint_t<T> * = nullptr>bool read_single(T &ref) {long long val = 0;bool f = read_single(val);ref = T(val);return f;}bool read_single(double &ref) {string s;if (!read_single(s)) return false;ref = std::stod(s);return true;}bool read_single(char &ref) {string s;if (!read_single(s) || s.size() != 1) return false;ref = s[0];return true;}template <class T>bool read_single(vector<T> &ref) {for (auto &d: ref) {if (!read_single(d)) return false;}return true;}template <class T, class U>bool read_single(pair<T, U> &p) {return (read_single(p.first) && read_single(p.second));}template <class A, class B, class C>bool read_single(tuple<A, B, C> &p) {return (read_single(get<0>(p)) && read_single(get<1>(p))&& read_single(get<2>(p)));}template <class A, class B, class C, class D>bool read_single(tuple<A, B, C, D> &p) {return (read_single(get<0>(p)) && read_single(get<1>(p))&& read_single(get<2>(p)) && read_single(get<3>(p)));}void read() {}template <class H, class... T>void read(H &h, T &... t) {bool f = read_single(h);assert(f);read(t...);}Scanner(FILE *fp) : fp(fp) {}};struct Printer {Printer(FILE *_fp) : fp(_fp) {}~Printer() { flush(); }static constexpr size_t SIZE = 1 << 15;FILE *fp;char line[SIZE], small[50];size_t pos = 0;void flush() {fwrite(line, 1, pos, fp);pos = 0;}void write(const char &val) {if (pos == SIZE) flush();line[pos++] = val;}template <class T, enable_if_t<is_integral<T>::value, int> = 0>void write(T val) {if (pos > (1 << 15) - 50) flush();if (val == 0) {write('0');return;}if (val < 0) {write('-');val = -val; // todo min}size_t len = 0;while (val) {small[len++] = char(0x30 | (val % 10));val /= 10;}for (size_t i = 0; i < len; i++) { line[pos + i] = small[len - 1 - i]; }pos += len;}void write(const string &s) {for (char c: s) write(c);}void write(const char *s) {size_t len = strlen(s);for (size_t i = 0; i < len; i++) write(s[i]);}void write(const double &x) {ostringstream oss;oss << setprecision(15) << x;string s = oss.str();write(s);}void write(const long double &x) {ostringstream oss;oss << setprecision(15) << x;string s = oss.str();write(s);}template <class T, is_modint_t<T> * = nullptr>void write(T &ref) {write(ref.val);}template <class T>void write(const vector<T> &val) {auto n = val.size();for (size_t i = 0; i < n; i++) {if (i) write(' ');write(val[i]);}}template <class T, class U>void write(const pair<T, U> &val) {write(val.first);write(' ');write(val.second);}template <class A, class B, class C>void write(const tuple<A, B, C> &val) {auto &[a, b, c] = val;write(a), write(' '), write(b), write(' '), write(c);}template <class A, class B, class C, class D>void write(const tuple<A, B, C, D> &val) {auto &[a, b, c, d] = val;write(a), write(' '), write(b), write(' '), write(c), write(' '), write(d);}template <class A, class B, class C, class D, class E>void write(const tuple<A, B, C, D, E> &val) {auto &[a, b, c, d, e] = val;write(a), write(' '), write(b), write(' '), write(c), write(' '), write(d), write(' '), write(e);}template <class A, class B, class C, class D, class E, class F>void write(const tuple<A, B, C, D, E, F> &val) {auto &[a, b, c, d, e, f] = val;write(a), write(' '), write(b), write(' '), write(c), write(' '), write(d), write(' '), write(e), write(' '), write(f);}template <class T, size_t S>void write(const array<T, S> &val) {auto n = val.size();for (size_t i = 0; i < n; i++) {if (i) write(' ');write(val[i]);}}void write(i128 val) {string s;bool negative = 0;if(val < 0){negative = 1;val = -val;}while (val) {s += '0' + int(val % 10);val /= 10;}if(negative) s += "-";reverse(all(s));if (len(s) == 0) s = "0";write(s);}};Scanner scanner = Scanner(stdin);Printer printer = Printer(stdout);void flush() { printer.flush(); }void print() { printer.write('\n'); }template <class Head, class... Tail>void print(Head &&head, Tail &&... tail) {printer.write(head);if (sizeof...(Tail)) printer.write(' ');print(forward<Tail>(tail)...);}void read() {}template <class Head, class... Tail>void read(Head &head, Tail &... tail) {scanner.read(head);read(tail...);}#define INT(...) \int __VA_ARGS__; \read(__VA_ARGS__)#define LL(...) \ll __VA_ARGS__; \read(__VA_ARGS__)#define STR(...) \string __VA_ARGS__; \read(__VA_ARGS__)#define CHAR(...) \char __VA_ARGS__; \read(__VA_ARGS__)#define DBL(...) \double __VA_ARGS__; \read(__VA_ARGS__)#define VEC(type, name, size) \vector<type> name(size); \read(name)#define VV(type, name, h, w) \vector<vector<type>> name(h, vector<type>(w)); \read(name)void YES(bool t = 1) { print(t ? "YES" : "NO"); }void NO(bool t = 1) { YES(!t); }void Yes(bool t = 1) { print(t ? "Yes" : "No"); }void No(bool t = 1) { Yes(!t); }void yes(bool t = 1) { print(t ? "yes" : "no"); }void no(bool t = 1) { yes(!t); }#line 2 "/home/maspy/compro/library/nt/primetest.hpp"struct m64 {using i64 = int64_t;using u64 = uint64_t;using u128 = __uint128_t;inline static u64 m, r, n2; // r * m = -1 (mod 1<<64), n2 = 1<<128 (mod m)static void set_mod(u64 m) {assert(m < (1ull << 62));assert((m & 1) == 1);m64::m = m;n2 = -u128(m) % m;r = m;FOR(_, 5) r *= 2 - m * r;r = -r;assert(r * m == -1ull);}static u64 reduce(u128 b) { return (b + u128(u64(b) * r) * m) >> 64; }u64 x;m64() : x(0) {}m64(u64 x) : x(reduce(u128(x) * n2)){};u64 val() const {u64 y = reduce(x);return y >= m ? y - m : y;}m64 &operator+=(m64 y) {x += y.x - (m << 1);x = (i64(x) < 0 ? x + (m << 1) : x);return *this;}m64 &operator-=(m64 y) {x -= y.x;x = (i64(x) < 0 ? x + (m << 1) : x);return *this;}m64 &operator*=(m64 y) {x = reduce(u128(x) * y.x);return *this;}m64 operator+(m64 y) const { return m64(*this) += y; }m64 operator-(m64 y) const { return m64(*this) -= y; }m64 operator*(m64 y) const { return m64(*this) *= y; }bool operator==(m64 y) const {return (x >= m ? x - m : x) == (y.x >= m ? y.x - m : y.x);}bool operator!=(m64 y) const { return not operator==(y); }m64 pow(u64 n) const {m64 y = 1, z = *this;for (; n; n >>= 1, z *= z)if (n & 1) y *= z;return y;}};bool primetest(const uint64_t x) {using u64 = uint64_t;if (x == 2 or x == 3 or x == 5 or x == 7) return true;if (x % 2 == 0 or x % 3 == 0 or x % 5 == 0 or x % 7 == 0) return false;if (x < 121) return x > 1;const u64 d = (x - 1) >> __builtin_ctzll(x - 1);m64::set_mod(x);const m64 one(1), minus_one(x - 1);auto ok = [&](u64 a) {auto y = m64(a).pow(d);u64 t = d;while (y != one and y != minus_one and t != x - 1) y *= y, t <<= 1;if (y != minus_one and t % 2 == 0) return false;return true;};if (x < (1ull << 32)) {for (u64 a: {2, 7, 61})if (not ok(a)) return false;} else {for (u64 a: {2, 325, 9375, 28178, 450775, 9780504, 1795265022}) {if (x <= a) return true;if (not ok(a)) return false;}}return true;}#line 3 "/home/maspy/compro/library/nt/factor.hpp"mt19937_64 rng_mt{random_device{}()};ll rnd(ll n) { return uniform_int_distribution<ll>(0, n - 1)(rng_mt); }ll rho(ll n, ll c) {m64::set_mod(n);assert(n > 1);const m64 cc(c);auto f = [&](m64 x) { return x * x + cc; };m64 x = 1, y = 2, z = 1, q = 1;ll g = 1;const ll m = 1LL << (__lg(n) / 5); // ?for (ll r = 1; g == 1; r <<= 1) {x = y;FOR(_, r) y = f(y);for (ll k = 0; k < r and g == 1; k += m) {z = y;FOR(_, min(m, r - k)) y = f(y), q *= x - y;g = gcd(q.val(), n);}}if (g == n)do {z = f(z);g = gcd((x - z).val(), n);} while (g == 1);return g;}ll find_prime_factor(ll n) {assert(n > 1);if (primetest(n))return n;FOR(_, 100) {ll m = rho(n, rnd(n));if (primetest(m))return m;n = m;}cerr << "failed" << endl;assert(false);return -1;}vc<pi> factor(ll n) {assert(n >= 1);vc<pi> pf;FOR3(p, 2, 100) {if (p * p > n)break;if (n % p == 0) {ll e = 0;do {n /= p, e += 1;} while (n % p == 0);pf.eb(p, e);}}while (n > 1) {ll p = find_prime_factor(n);ll e = 0;do {n /= p, e += 1;} while (n % p == 0);pf.eb(p, e);}sort(all(pf));return pf;}#line 2 "/home/maspy/compro/library/mod/modint.hpp"template <u32 mod>struct modint {static constexpr bool is_modint = true;u32 val;constexpr modint(const ll val = 0) noexcept: val(val >= 0 ? val % mod : (mod - (-val) % mod) % mod) {}bool operator<(const modint &other) const {return val < other.val;} // To use std::mapmodint &operator+=(const modint &p) {if ((val += p.val) >= mod) val -= mod;return *this;}modint &operator-=(const modint &p) {if ((val += mod - p.val) >= mod) val -= mod;return *this;}modint &operator*=(const modint &p) {val = (u32)(1LL * val * p.val % mod);return *this;}modint &operator/=(const modint &p) {*this *= p.inverse();return *this;}modint operator-() const { return modint(get_mod() - val); }modint operator+(const modint &p) const { return modint(*this) += p; }modint operator-(const modint &p) const { return modint(*this) -= p; }modint operator*(const modint &p) const { return modint(*this) *= p; }modint operator/(const modint &p) const { return modint(*this) /= p; }bool operator==(const modint &p) const { return val == p.val; }bool operator!=(const modint &p) const { return val != p.val; }modint inverse() const {int a = val, b = mod, u = 1, v = 0, t;while (b > 0) {t = a / b;swap(a -= t * b, b), swap(u -= t * v, v);}return modint(u);}modint pow(int64_t n) const {modint ret(1), mul(val);while (n > 0) {if (n & 1) ret *= mul;mul *= mul;n >>= 1;}return ret;}static constexpr u32 get_mod() { return mod; }};struct ArbitraryModInt {static constexpr bool is_modint = true;u32 val;ArbitraryModInt() : val(0) {}ArbitraryModInt(int64_t y): val(y >= 0 ? y % get_mod(): (get_mod() - (-y) % get_mod()) % get_mod()) {}bool operator<(const ArbitraryModInt &other) const {return val < other.val;} // To use std::map<ArbitraryModInt, T>static u32 &get_mod() {static u32 mod = 0;return mod;}static void set_mod(int md) { get_mod() = md; }ArbitraryModInt &operator+=(const ArbitraryModInt &p) {if ((val += p.val) >= get_mod()) val -= get_mod();return *this;}ArbitraryModInt &operator-=(const ArbitraryModInt &p) {if ((val += get_mod() - p.val) >= get_mod()) val -= get_mod();return *this;}ArbitraryModInt &operator*=(const ArbitraryModInt &p) {unsigned long long a = (unsigned long long)val * p.val;unsigned xh = (unsigned)(a >> 32), xl = (unsigned)a, d, m;asm("divl %4; \n\t" : "=a"(d), "=d"(m) : "d"(xh), "a"(xl), "r"(get_mod()));val = m;return *this;}ArbitraryModInt &operator/=(const ArbitraryModInt &p) {*this *= p.inverse();return *this;}ArbitraryModInt operator-() const { return ArbitraryModInt(get_mod() - val); }ArbitraryModInt operator+(const ArbitraryModInt &p) const {return ArbitraryModInt(*this) += p;}ArbitraryModInt operator-(const ArbitraryModInt &p) const {return ArbitraryModInt(*this) -= p;}ArbitraryModInt operator*(const ArbitraryModInt &p) const {return ArbitraryModInt(*this) *= p;}ArbitraryModInt operator/(const ArbitraryModInt &p) const {return ArbitraryModInt(*this) /= p;}bool operator==(const ArbitraryModInt &p) const { return val == p.val; }bool operator!=(const ArbitraryModInt &p) const { return val != p.val; }ArbitraryModInt inverse() const {int a = val, b = get_mod(), u = 1, v = 0, t;while (b > 0) {t = a / b;swap(a -= t * b, b), swap(u -= t * v, v);}return ArbitraryModInt(u);}ArbitraryModInt pow(int64_t n) const {ArbitraryModInt ret(1), mul(val);while (n > 0) {if (n & 1) ret *= mul;mul *= mul;n >>= 1;}return ret;}};template <typename mint>tuple<mint, mint, mint> get_factorial_data(int n) {static const int mod = mint::get_mod();assert(0 <= n && n < mod);static vector<mint> fact = {1, 1};static vector<mint> fact_inv = {1, 1};static vector<mint> inv = {0, 1};while (len(fact) <= n) {int k = len(fact);fact.eb(fact[k - 1] * mint(k));auto q = ceil(mod, k);int r = k * q - mod;inv.eb(inv[r] * mint(q));fact_inv.eb(fact_inv[k - 1] * inv[k]);}return {fact[n], fact_inv[n], inv[n]};}template <typename mint>mint fact(int n) {static const int mod = mint::get_mod();assert(0 <= n);if (n >= mod) return 0;return get<0>(get_factorial_data<mint>(n));}template <typename mint>mint fact_inv(int n) {static const int mod = mint::get_mod();assert(0 <= n && n < mod);return get<1>(get_factorial_data<mint>(n));}template <typename mint>mint inv(int n) {static const int mod = mint::get_mod();assert(0 <= n && n < mod);return get<2>(get_factorial_data<mint>(n));}template <typename mint, bool large = false>mint C(ll n, ll k) {assert(n >= 0);if (k < 0 || n < k) return 0;if (!large) return fact<mint>(n) * fact_inv<mint>(k) * fact_inv<mint>(n - k);k = min(k, n - k);mint x(1);FOR(i, k) { x *= mint(n - i); }x *= fact_inv<mint>(k);return x;}template <typename mint, bool large = false>mint C_inv(ll n, ll k) {assert(n >= 0);assert(0 <= k && k <= n);if (!large) return fact_inv<mint>(n) * fact<mint>(k) * fact<mint>(n - k);return mint(1) / C<mint, 1>(n, k);}using modint107 = modint<1000000007>;using modint998 = modint<998244353>;using amint = ArbitraryModInt;#line 2 "/home/maspy/compro/library/nt/primetable.hpp"vc<ll> primetable(int LIM) {++LIM;const int S = 32768;static int done = 2;static vc<ll> primes = {2}, sieve(S + 1);if (done < LIM) {done = LIM;primes = {2}, sieve.assign(S + 1, 0);const int R = LIM / 2;primes.reserve(int(LIM / log(LIM) * 1.1));vc<pi> cp;for (int i = 3; i <= S; i += 2) {if (!sieve[i]) {cp.eb(i, i * i / 2);for (int j = i * i; j <= S; j += 2 * i) sieve[j] = 1;}}for (int L = 1; L <= R; L += S) {array<bool, S> block{};for (auto& [p, idx]: cp)for (int i = idx; i < S + L; idx = (i += p)) block[i - L] = 1;FOR(i, min(S, R - L)) if (!block[i]) primes.eb((L + i) * 2 + 1);}}int k = LB(primes, LIM + 1);return {primes.begin(), primes.begin() + k};}#line 1 "/home/maspy/compro/library/mod/mod_inv.hpp"// long でも大丈夫ll mod_inv(ll val, ll mod) {ll a = val, b = mod, u = 1, v = 0, t;while (b > 0) {t = a / b;swap(a -= t * b, b), swap(u -= t * v, v);}if(u < 0) u += mod;return u;}#line 7 "main.cpp"using mint = modint998;void solve() {LL(N);VEC(pi, AB, N);mint C = 0;for (auto&& [a, b]: AB) C += mint(a) * inv<mint>(b);ll LIM = 200200;// 分母 -> 分子vvc<int> dat(LIM);for (auto&& [a, b]: AB) dat[b].eb(a);mint D = 1;for (auto&& p: primetable(LIM)) {ll e = 0;ll pp = 1;while (pp * p <= LIM) {pp *= p;e += 1;}// pp を分母にしたときの、mod pp での値ll x = 0;ll den = p;while (den < LIM) {for (auto&& a: dat[den]) {// a / denll g = gcd(a * pp, den);ll s = a * pp / g;ll t = den / g;x += s * mod_inv(t, pp) % pp;}den += p;}D *= mint(pp / gcd(pp, x));}C *= D;print(C, D);}signed main() {cin.tie(nullptr);ios::sync_with_stdio(false);cout << setprecision(15);ll T = 1;// LL(T);FOR(_, T) solve();return 0;}