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:x: nt/lcm_convolution.hpp

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Code

#include "nt/zeta.hpp"

template <typename T>
vc<T> lcm_convolution(vc<T> A, vc<T>& B) {
  assert(len(A) == len(B));
  divisor_zeta(A);
  divisor_zeta(B);
  FOR(i, len(A)) A[i] *= B[i];
  divisor_mobius(A);
  return A;
}
#line 2 "nt/primetable.hpp"

template <typename T = int>
vc<T> primetable(int LIM) {
  ++LIM;
  const int S = 32768;
  static int done = 2;
  static vc<T> 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<pair<int, int>> 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 3 "nt/zeta.hpp"

template <typename T>
void divisor_zeta(vc<T>& A) {
  assert(A[0] == 0);
  int N = len(A) - 1;
  auto P = primetable(N);
  for (auto&& p: P) { FOR3(x, 1, N / p + 1) A[p * x] += A[x]; }
}

template <typename T>
void divisor_mobius(vc<T>& A) {
  assert(A[0] == 0);
  int N = len(A) - 1;
  auto P = primetable(N);
  for (auto&& p: P) { FOR3_R(x, 1, N / p + 1) A[p * x] -= A[x]; }
}

template <typename T>
void multiplier_zeta(vc<T>& A) {
  assert(A[0] == 0);
  int N = len(A) - 1;
  auto P = primetable(N);
  for (auto&& p: P) { FOR3_R(x, 1, N / p + 1) A[x] += A[p * x]; }
}

template <typename T>
void multiplier_mobius(vc<T>& A) {
  assert(A[0] == 0);
  int N = len(A) - 1;
  auto P = primetable(N);
  for (auto&& p: P) { FOR3(x, 1, N / p + 1) A[x] -= A[p * x]; }
}
#line 2 "nt/lcm_convolution.hpp"

template <typename T>
vc<T> lcm_convolution(vc<T> A, vc<T>& B) {
  assert(len(A) == len(B));
  divisor_zeta(A);
  divisor_zeta(B);
  FOR(i, len(A)) A[i] *= B[i];
  divisor_mobius(A);
  return A;
}
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