#include <iostream>
#include <algorithm>
#include <vector>
#include <string>
#include <random>
#include <ctime>
 
using namespace std;
 
const int mod = 1e9 + 7;
 
struct mint {
  int n;
  mint(int n_ = 0) : n(n_) {}
};
 
mint operator+(mint a, mint b) { return (a.n += b.n) >= mod ? a.n - mod : a.n; }
mint operator-(mint a, mint b) { return (a.n -= b.n) < 0 ? a.n + mod : a.n; }
mint operator*(mint a, mint b) { return 1LL * a.n * b.n % mod; }
mint &operator+=(mint &a, mint b) { return a = a + b; }
mint &operator-=(mint &a, mint b) { return a = a - b; }
mint &operator*=(mint &a, mint b) { return a = a * b; }
ostream &operator<<(ostream &o, mint a) { return o << a.n; }
 
int gcd(int x, int y) {
  while (y != 0) {
    int r = x % y;
    x = y;
    y = r;
  }
  return x;
}
 
int lcm(int x, int y) {
  return x / gcd(x, y) * y;
}
 
 
vector<mint> zeta(vector<mint> a) {
  const int n = a.size();
  for (int i = 1; i < n; i++) {
    for (int j = i * 2; j < n; j += i) {
      a[i] += a[j];
    }
  }
  return a;
}
 
vector<mint> mobius(vector<mint> a) {
  const int n = a.size();
  for (int i = n - 1; i >= 1; i--) {
    for (int j = i * 2; j < n; j += i) {
      a[i] -= a[j];
    }
  }
  return a;
}
 
vector<mint> zeta2(vector<mint> a) {
  const int n = a.size();
  for (int i = n - 1; i >= 1; i--) {
    for (int j = i * 2; j < n; j += i) {
      a[j] += a[i];
    }
  }
  return a;
}
 
vector<mint> mobius2(vector<mint> a) {
  const int n = a.size();
  for (int i = 1; i < n; i++) {
    for (int j = i * 2; j < n; j += i) {
      a[j] -= a[i];
    }
  }
  return a;
}
 
vector<mint> conv(vector<mint> a, vector<mint> b) {
  const int n = a.size();
  vector<mint> res(n);
  for (int i = 1; i < n; i++) {
    for (int j = 1; j < n; j++) {
      res[gcd(i, j)] += a[i] * b[j];
    }
  }
  return res;
}
 
vector<mint> conv2(vector<mint> a, vector<mint> b) {
  const int n = a.size();
  vector<mint> res(n);
  for (int i = 1; i < n; i++) {
    for (int j = 1; j < n; j++) {
      int l = lcm(i, j);
      if (l < n) {
        res[l] += a[i] * b[j];
      }
    }
  }
  return res;
}
 
void solve1() {
  cout << "gcd" << endl;
  vector<mint> a(100);
  for (int i = 1; i < 100; i++) {
    a[i] = i;
  }
  auto ans = conv(a, a);
  a = zeta(a);
  for (int i = 1; i < 100; i++) {
    a[i] *= a[i];
  }
  a = mobius(a);
  for (int i = 1; i < 100; i++) {
    cout << i << ' ' << a[i] << ' ' << ans[i] << endl;
  }
  cout << endl;
}
 
void solve2() {
  cout << "lcm" << endl;
  vector<mint> a(100);
  for (int i = 1; i < 100; i++) {
    a[i] = i;
  }
  auto ans = conv2(a, a);
  a = zeta2(a);
  for (int i = 1; i < 100; i++) {
    a[i] *= a[i];
  }
  a = mobius2(a);
  for (int i = 1; i < 100; i++) {
    cout << i << ' ' << a[i] << ' ' << ans[i] << endl;
  }
  cout << endl;
}
 
int main() {
  solve1();
  solve2();
}
 
 

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