Hashiryo's Library

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:warning: test/atcoder/abc335_g.test.cpp

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// competitive-verifier: IGNORE
// competitive-verifier: PROBLEM https://atcoder.jp/contests/abc335/tasks/abc335_g
// competitive-verifier: TLE 0.5
// competitive-verifier: MLE 64
#include <iostream>
#include "src/NumberTheory/OrderFp.hpp"
#include "src/NumberTheory/ArrayOnDivisors.hpp"
using namespace std;
signed main() {
 cin.tie(0);
 ios::sync_with_stdio(false);
 long long N, P;
 cin >> N >> P;
 vector<long long> a(N);
 OrderFp ord(P);
 for (int i= 0; i < N; i++) {
  long long A;
  cin >> A;
  a[i]= ord(A);
 }
 ArrayOnDivisors<long long, long long> x(P - 1, ord.factors);
 for (int i= 0; i < N; ++i) ++x[a[i]];
 x.divisor_zeta();
 long long ans= 0;
 for (int i= 0; i < N; ++i) ans+= x[a[i]];
 cout << ans << '\n';
 return 0;
}
#line 1 "test/atcoder/abc335_g.test.cpp"
// competitive-verifier: IGNORE
// competitive-verifier: PROBLEM https://atcoder.jp/contests/abc335/tasks/abc335_g
// competitive-verifier: TLE 0.5
// competitive-verifier: MLE 64
#include <iostream>
#line 2 "src/NumberTheory/OrderFp.hpp"
#include <array>
#line 2 "src/NumberTheory/Factors.hpp"
#include <numeric>
#include <cassert>
#line 5 "src/NumberTheory/Factors.hpp"
#include <algorithm>
#include <vector>
#line 2 "src/Internal/Remainder.hpp"
namespace math_internal {
using namespace std;
using u8= unsigned char;
using u32= unsigned;
using i64= long long;
using u64= unsigned long long;
using u128= __uint128_t;
struct MP_Na {  // mod < 2^32
 u32 mod;
 constexpr MP_Na(): mod(0) {}
 constexpr MP_Na(u32 m): mod(m) {}
 constexpr inline u32 mul(u32 l, u32 r) const { return u64(l) * r % mod; }
 constexpr inline u32 set(u32 n) const { return n; }
 constexpr inline u32 get(u32 n) const { return n; }
 constexpr inline u32 norm(u32 n) const { return n; }
 constexpr inline u32 plus(u64 l, u32 r) const { return l+= r, l < mod ? l : l - mod; }
 constexpr inline u32 diff(u64 l, u32 r) const { return l-= r, l >> 63 ? l + mod : l; }
};
template <class u_t, class du_t, u8 B> struct MP_Mo {  // mod < 2^32, mod < 2^62
 u_t mod;
 constexpr MP_Mo(): mod(0), iv(0), r2(0) {}
 constexpr MP_Mo(u_t m): mod(m), iv(inv(m)), r2(-du_t(mod) % mod) {}
 constexpr inline u_t mul(u_t l, u_t r) const { return reduce(du_t(l) * r); }
 constexpr inline u_t set(u_t n) const { return mul(n, r2); }
 constexpr inline u_t get(u_t n) const { return n= reduce(n), n >= mod ? n - mod : n; }
 constexpr inline u_t norm(u_t n) const { return n >= mod ? n - mod : n; }
 constexpr inline u_t plus(u_t l, u_t r) const { return l+= r, l < (mod << 1) ? l : l - (mod << 1); }
 constexpr inline u_t diff(u_t l, u_t r) const { return l-= r, l >> (B - 1) ? l + (mod << 1) : l; }
private:
 u_t iv, r2;
 static constexpr u_t inv(u_t n, int e= 6, u_t x= 1) { return e ? inv(n, e - 1, x * (2 - x * n)) : x; }
 constexpr inline u_t reduce(const du_t &w) const { return u_t(w >> B) + mod - ((du_t(u_t(w) * iv) * mod) >> B); }
};
using MP_Mo32= MP_Mo<u32, u64, 32>;
using MP_Mo64= MP_Mo<u64, u128, 64>;
struct MP_Br {  // 2^20 < mod <= 2^41
 u64 mod;
 constexpr MP_Br(): mod(0), x(0) {}
 constexpr MP_Br(u64 m): mod(m), x((u128(1) << 84) / m) {}
 constexpr inline u64 mul(u64 l, u64 r) const { return rem(u128(l) * r); }
 static constexpr inline u64 set(u64 n) { return n; }
 constexpr inline u64 get(u64 n) const { return n >= mod ? n - mod : n; }
 constexpr inline u64 norm(u64 n) const { return n >= mod ? n - mod : n; }
 constexpr inline u64 plus(u64 l, u64 r) const { return l+= r, l < (mod << 1) ? l : l - (mod << 1); }
 constexpr inline u64 diff(u64 l, u64 r) const { return l-= r, l >> 63 ? l + (mod << 1) : l; }
private:
 u64 x;
 constexpr inline u128 quo(const u128 &n) const { return (n * x) >> 84; }
 constexpr inline u64 rem(const u128 &n) const { return n - quo(n) * mod; }
};
template <class du_t, u8 B> struct MP_D2B1 {  // mod < 2^63, mod < 2^64
 u64 mod;
 constexpr MP_D2B1(): mod(0), s(0), d(0), v(0) {}
 constexpr MP_D2B1(u64 m): mod(m), s(__builtin_clzll(m)), d(m << s), v(u128(-1) / d) {}
 constexpr inline u64 mul(u64 l, u64 r) const { return rem((u128(l) * r) << s) >> s; }
 constexpr inline u64 set(u64 n) const { return n; }
 constexpr inline u64 get(u64 n) const { return n; }
 constexpr inline u64 norm(u64 n) const { return n; }
 constexpr inline u64 plus(du_t l, u64 r) const { return l+= r, l < mod ? l : l - mod; }
 constexpr inline u64 diff(du_t l, u64 r) const { return l-= r, l >> B ? l + mod : l; }
private:
 u8 s;
 u64 d, v;
 constexpr inline u64 rem(const u128 &u) const {
  u128 q= (u >> 64) * v + u;
  u64 r= u64(u) - (q >> 64) * d - d;
  if (r > u64(q)) r+= d;
  if (r >= d) r-= d;
  return r;
 }
};
using MP_D2B1_1= MP_D2B1<u64, 63>;
using MP_D2B1_2= MP_D2B1<u128, 127>;
template <class u_t, class MP> constexpr u_t pow(u_t x, u64 k, const MP &md) {
 for (u_t ret= md.set(1);; x= md.mul(x, x))
  if (k & 1 ? ret= md.mul(ret, x) : 0; !(k>>= 1)) return ret;
}
}
#line 3 "src/NumberTheory/is_prime.hpp"
namespace math_internal {
template <class Uint, class MP, u32... args> constexpr bool miller_rabin(Uint n) {
 const MP md(n);
 const Uint s= __builtin_ctzll(n - 1), d= n >> s, one= md.set(1), n1= md.norm(md.set(n - 1));
 for (u32 a: (u32[]){args...})
  if (Uint b= a % n; b)
   if (Uint p= md.norm(pow(md.set(b), d, md)); p != one)
    for (int i= s; p != n1; p= md.norm(md.mul(p, p)))
     if (!(--i)) return 0;
 return 1;
}
}
constexpr bool is_prime(unsigned long long n) {
 if (n < 2 || n % 6 % 4 != 1) return (n | 1) == 3;
 if (n < (1 << 30)) return math_internal::miller_rabin<unsigned, math_internal::MP_Mo32, 2, 7, 61>(n);
 if (n < (1ull << 62)) return math_internal::miller_rabin<unsigned long long, math_internal::MP_Mo64, 2, 325, 9375, 28178, 450775, 9780504, 1795265022>(n);
 if (n < (1ull << 63)) return math_internal::miller_rabin<unsigned long long, math_internal::MP_D2B1_1, 2, 325, 9375, 28178, 450775, 9780504, 1795265022>(n);
 return math_internal::miller_rabin<unsigned long long, math_internal::MP_D2B1_2, 2, 325, 9375, 28178, 450775, 9780504, 1795265022>(n);
}
#line 2 "src/Math/binary_gcd.hpp"
#include <type_traits>
#line 4 "src/Math/binary_gcd.hpp"
#include <cstdint>
template <class Int> constexpr int bsf(Int a) {
 if constexpr (sizeof(Int) == 16) {
  uint64_t lo= a & uint64_t(-1);
  return lo ? __builtin_ctzll(lo) : 64 + __builtin_ctzll(a >> 64);
 } else if constexpr (sizeof(Int) == 8) return __builtin_ctzll(a);
 else return __builtin_ctz(a);
}
template <class Int> constexpr Int binary_gcd(Int a, Int b) {
 if (a == 0 || b == 0) return a + b;
 int n= bsf(a), m= bsf(b), s= 0;
 for (a>>= n, b>>= m; a != b;) {
  Int d= a - b;
  bool f= a > b;
  s= bsf(d), b= f ? b : a, a= (f ? d : -d) >> s;
 }
 return a << std::min(n, m);
}
#line 9 "src/NumberTheory/Factors.hpp"
namespace math_internal {
template <class T> constexpr void bubble_sort(T *bg, T *ed) {
 for (int sz= ed - bg, i= 0; i < sz; i++)
  for (int j= sz; --j > i;)
   if (auto tmp= bg[j - 1]; bg[j - 1] > bg[j]) bg[j - 1]= bg[j], bg[j]= tmp;
}
template <class T, size_t _Nm> struct ConstexprArray {
 constexpr size_t size() const { return sz; }
 constexpr auto &operator[](int i) const { return dat[i]; }
 constexpr auto *begin() const { return dat; }
 constexpr auto *end() const { return dat + sz; }
protected:
 T dat[_Nm]= {};
 size_t sz= 0;
 friend ostream &operator<<(ostream &os, const ConstexprArray &r) {
  os << "[";
  for (size_t i= 0; i < r.sz; ++i) os << r[i] << ",]"[i == r.sz - 1];
  return os;
 }
};
class Factors: public ConstexprArray<pair<u64, uint16_t>, 16> {
 template <class Uint, class MP> static constexpr Uint rho(Uint n, Uint c) {
  const MP md(n);
  auto f= [&md, c](Uint x) { return md.plus(md.mul(x, x), c); };
  const Uint m= 1LL << (__lg(n) / 5);
  Uint x= 1, y= md.set(2), z= 1, q= md.set(1), g= 1;
  for (Uint r= 1, i= 0; g == 1; r<<= 1) {
   for (x= y, i= r; i--;) y= f(y);
   for (Uint k= 0; k < r && g == 1; g= binary_gcd<Uint>(md.get(q), n), k+= m)
    for (z= y, i= min(m, r - k); i--;) y= f(y), q= md.mul(q, md.diff(y, x));
  }
  if (g == n) do {
    z= f(z), g= binary_gcd<Uint>(md.get(md.diff(z, x)), n);
   } while (g == 1);
  return g;
 }
 static constexpr u64 find_prime_factor(u64 n) {
  if (is_prime(n)) return n;
  for (u64 i= 100; i--;)
   if (n= n < (1 << 30) ? rho<u32, MP_Mo32>(n, i + 1) : n < (1ull << 62) ? rho<u64, MP_Mo64>(n, i + 1) : n < (1ull << 62) ? rho<u64, MP_D2B1_1>(n, i + 1) : rho<u64, MP_D2B1_2>(n, i + 1); is_prime(n)) return n;
  return 0;
 }
 constexpr void init(u64 n) {
  for (u64 p= 2; p < 98 && p * p <= n; ++p)
   if (n % p == 0)
    for (dat[sz++].first= p; n % p == 0;) n/= p, ++dat[sz - 1].second;
  for (u64 p= 0; n > 1; dat[sz++].first= p)
   for (p= find_prime_factor(n); n % p == 0;) n/= p, ++dat[sz].second;
 }
public:
 constexpr Factors()= default;
 constexpr Factors(u64 n) { init(n), bubble_sort(dat, dat + sz); }
};
}
using math_internal::Factors;
constexpr uint64_t totient(const Factors &f) {
 uint64_t ret= 1, i= 0;
 for (auto [p, e]: f)
  for (ret*= p - 1, i= e; --i;) ret*= p;
 return ret;
}
constexpr auto totient(uint64_t n) { return totient(Factors(n)); }
template <class Uint= uint64_t> std::vector<Uint> enumerate_divisors(const Factors &f) {
 int k= 1;
 for (auto [p, e]: f) k*= e + 1;
 std::vector<Uint> ret(k, 1);
 k= 1;
 for (auto [p, e]: f) {
  int sz= k;
  for (Uint pw= 1; pw*= p, e--;)
   for (int j= 0; j < sz;) ret[k++]= ret[j++] * pw;
 }
 return ret;
}
template <class Uint> std::vector<Uint> enumerate_divisors(Uint n) { return enumerate_divisors<Uint>(Factors(n)); }
#line 4 "src/NumberTheory/OrderFp.hpp"
namespace math_internal {
class OrderFp {
 u64 p;
 std::array<u64, 17> prod;
 template <class Uint, class MP> constexpr Uint p_rt() const {
  const MP md(p);
  for (Uint ret= 2, one= md.set(1), ng= 0, m= p - 1;; ++ret) {
   Uint a= md.set(ret);
   for (auto [q, e]: factors)
    if ((ng= (md.norm(pow(a, m / q, md)) == one))) break;
   if (!ng) return ret;
  }
 }
 template <class Uint, class MP> constexpr Uint ord_(u8 l, u8 r, Uint x, const MP &md) const {
  Uint ret= 1;
  if (r - l == 1) {
   Uint one= md.set(1);
   auto [q, e]= factors[l];
   for (u8 i= e; i--; ret*= q, x= pow(x, q, md))
    if (x == one) break;
   return ret;
  }
  u8 m= (l + r) / 2;
  return ord_(l, m, pow(x, prod[r] / prod[m], md), md) * ord_(m, r, pow(x, prod[m] / prod[l], md), md);
 }
 template <class Uint, class MP> constexpr Uint ord(Uint x) const {
  const MP md(p);
  return ord_(0, factors.size(), md.set(x), md);
 }
public:
 Factors factors;
 constexpr OrderFp(u64 p): p(p), prod({1}), factors(p - 1) {
  assert(is_prime(p));
  for (u8 i= 0, d= factors.size(); i < d; ++i) {
   auto [q, e]= factors[i];
   prod[i + 1]= prod[i];
   for (u8 j= e; j--;) prod[i + 1]*= q;
  }
 }
 constexpr u64 primitive_root() const {
  if (p == 2) return 1;
  if (p < (1 << 30)) return p_rt<u32, MP_Mo32>();
  if (p < (1ull << 62)) return p_rt<u64, MP_Mo64>();
  if (p < (1ull << 63)) return p_rt<u64, MP_D2B1_1>();
  return p_rt<u64, MP_D2B1_2>();
 }
 constexpr u64 operator()(u64 x) const {
  if (x%= p; !x) return 0;
  if (x == 1) return 1;
  if (p < (1 << 30)) return ord<u32, MP_Mo32>(x);
  if (p < (1ull << 62)) return ord<u64, MP_Mo64>(x);
  if (p < (1ull << 63)) return ord<u64, MP_D2B1_1>(x);
  return ord<u64, MP_D2B1_2>(x);
 }
};
}
using math_internal::OrderFp;
#line 3 "src/NumberTheory/ArrayOnDivisors.hpp"
template <class Int, class T> struct ArrayOnDivisors {
 using Hint= std::conditional_t<sizeof(Int) == 8, unsigned, uint16_t>;
 Int n;
 uint8_t shift;
 std::vector<Hint> os, id;
 std::vector<std::pair<Int, T>> dat;
 Hint hash(uint64_t i) const { return (i * 11995408973635179863ULL) >> shift; }
#define _UP for (int j= k; j < a; ++j)
#define _DWN for (int j= a; j-- > k;)
#define _OP(J, K, op) dat[i + J].second op##= dat[i + K].second
#define _FUN(J, K, name) name(dat[i + J].second, dat[i + K].second)
#define _ZETA(op) \
 int k= 1; \
 for (auto [p, e]: factors) { \
  int a= k * (e + 1); \
  for (int i= 0, d= dat.size(); i < d; i+= a) op; \
  k= a; \
 }
public:
 Factors factors;
 ArrayOnDivisors() {}
 template <class Uint> ArrayOnDivisors(Int N, const Factors &factors, const std::vector<Uint> &divisors): n(N), shift(__builtin_clzll(divisors.size()) - 1), os((1 << (64 - shift)) + 1), id(divisors.size()), dat(divisors.size()), factors(factors) {
  static_assert(std::is_integral_v<Uint>, "Uint must be integral");
  int m= divisors.size(), i= 0;
  for (; i < m; ++i) ++os[hash(dat[i].first= divisors[i])];
  for (std::partial_sum(os.begin(), os.end(), os.begin()); i--;) id[--os[hash(divisors[i])]]= i;
 }
 ArrayOnDivisors(Int N, const Factors &factors): ArrayOnDivisors(N, factors, enumerate_divisors(factors)) {}
 ArrayOnDivisors(Int N): ArrayOnDivisors(N, Factors(N)) {}
 T &operator[](Int i) {
  assert(i && n % i == 0);
  for (unsigned a= hash(i), j= os[a]; j < os[a + 1]; ++j)
   if (auto &[d, v]= dat[id[j]]; d == i) return v;
  assert(0);
 }
 const T &operator[](Int i) const {
  assert(i && n % i == 0);
  for (unsigned a= hash(i), j= os[a]; j < os[a + 1]; ++j)
   if (auto &[d, v]= dat[id[j]]; d == i) return v;
  assert(0);
 }
 size_t size() const { return dat.size(); }
 auto begin() { return dat.begin(); }
 auto begin() const { return dat.begin(); }
 auto end() { return dat.begin() + os.back(); }
 auto end() const { return dat.begin() + os.back(); }
 /* f -> g s.t. g(n) = sum_{m|n} f(m) */
 void divisor_zeta() { _ZETA(_UP _OP(j, j - k, +)) }
 /* f -> h s.t. f(n) = sum_{m|n} h(m) */
 void divisor_mobius() { _ZETA(_DWN _OP(j, j - k, -)) }
 /* f -> g s.t. g(n) = sum_{n|m} f(m) */
 void multiple_zeta() { _ZETA(_DWN _OP(j - k, j, +)) }
 /* f -> h s.t. f(n) = sum_{n|m} h(m) */
 void multiple_mobius() { _ZETA(_UP _OP(j - k, j, -)) }
 /* f -> g s.t. g(n) = sum_{m|n} f(m), add(T& a, T b): a+=b */
 template <class F> void divisor_zeta(const F &add) { _ZETA(_UP _FUN(j, j - k, add)) }
 /* f -> h s.t. f(n) = sum_{m|n} h(m), sub(T& a, T b): a-=b */
 template <class F> void divisor_mobius(const F &sub) { _ZETA(_UP _FUN(j, j - k, sub)) }
 /* f -> g s.t. g(n) = sum_{n|m} f(m), add(T& a, T b): a+=b */
 template <class F> void multiple_zeta(const F &add) { _ZETA(_UP _FUN(j - k, j, add)) }
 /* f -> h s.t. f(n) = sum_{n|m} h(m), sub(T& a, T b): a-=b */
 template <class F> void multiple_mobius(const F &sub) { _ZETA(_UP _FUN(j - k, j, sub)) }
#undef _UP
#undef _DWN
#undef _OP
#undef _ZETA
 // f(p,e): multiplicative function of p^e
 template <typename F> void set_multiplicative(const F &f) {
  int k= 1;
  dat[0].second= 1;
  for (auto [p, e]: factors)
   for (int m= k, d= 1; d <= e; ++d)
    for (int i= 0; i < m;) dat[k++].second= dat[i++].second * f(p, d);
 }
 void set_totient() {
  int k= 1;
  dat[0].second= 1;
  for (auto [p, e]: factors) {
   Int b= p - 1;
   for (int m= k; e--; b*= p)
    for (int i= 0; i < m;) dat[k++].second= dat[i++].second * b;
  }
 }
 void set_mobius() {
  set_multiplicative([](auto, auto e) { return e == 1 ? -1 : 0; });
 }
};
#line 8 "test/atcoder/abc335_g.test.cpp"
using namespace std;
signed main() {
 cin.tie(0);
 ios::sync_with_stdio(false);
 long long N, P;
 cin >> N >> P;
 vector<long long> a(N);
 OrderFp ord(P);
 for (int i= 0; i < N; i++) {
  long long A;
  cin >> A;
  a[i]= ord(A);
 }
 ArrayOnDivisors<long long, long long> x(P - 1, ord.factors);
 for (int i= 0; i < N; ++i) ++x[a[i]];
 x.divisor_zeta();
 long long ans= 0;
 for (int i= 0; i < N; ++i) ans+= x[a[i]];
 cout << ans << '\n';
 return 0;
}
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