#include <bits/stdc++.h>
using namespace std;
template <typename A, typename B>
string to_string(pair<A, B> p);
template <typename A, typename B, typename C>
string to_string(tuple<A, B, C> p);
template <typename A, typename B, typename C, typename D>
string to_string(tuple<A, B, C, D> p);
string to_string(const string& s) { return '"' + s + '"'; }
string to_string(const char* s) { return to_string((string)s); }
string to_string(bool b) { return (b ? "true" : "false"); }
string to_string(vector<bool> v) {
  bool first = true;
  string res = "{";
  for (int i = 0; i < static_cast<int>(v.size()); i++) {
    if (!first) {
      res += ", ";
    }
    first = false;
    res += to_string(v[i]);
  }
  res += "}";
  return res;
}
template <size_t N>
string to_string(bitset<N> v) {
  string res = "";
  for (size_t i = 0; i < N; i++) {
    res += static_cast<char>('0' + v[i]);
  }
  return res;
}
template <typename A>
string to_string(A v) {
  bool first = true;
  string res = "{";
  for (const auto& x : v) {
    if (!first) {
      res += ", ";
    }
    first = false;
    res += to_string(x);
  }
  res += "}";
  return res;
}
template <typename A, typename B>
string to_string(pair<A, B> p) {
  return "(" + to_string(p.first) + ", " + to_string(p.second) + ")";
}
template <typename A, typename B, typename C>
string to_string(tuple<A, B, C> p) {
  return "(" + to_string(get<0>(p)) + ", " + to_string(get<1>(p)) + ", " +
         to_string(get<2>(p)) + ")";
}
template <typename A, typename B, typename C, typename D>
string to_string(tuple<A, B, C, D> p) {
  return "(" + to_string(get<0>(p)) + ", " + to_string(get<1>(p)) + ", " +
         to_string(get<2>(p)) + ", " + to_string(get<3>(p)) + ")";
}
void debug_out() { cerr << endl; }
template <typename Head, typename... Tail>
void debug_out(Head H, Tail... T) {
  cerr << " " << to_string(H);
  debug_out(T...);
}
template <typename T>
T inverse(T a, T m) {
  T u = 0, v = 1;
  while (a != 0) {
    T t = m / a;
    m -= t * a;
    swap(a, m);
    u -= t * v;
    swap(u, v);
  }
  assert(m == 1);
  return u;
}
template <typename T>
class Modular {
 public:
  using Type = typename decay<decltype(T::value)>::type;
  constexpr Modular() : value() {}
  template <typename U>
  Modular(const U& x) {
    value = normalize(x);
  }
  template <typename U>
  static Type normalize(const U& x) {
    Type v;
    if (-mod() <= x && x < mod())
      v = static_cast<Type>(x);
    else
      v = static_cast<Type>(x % mod());
    if (v < 0) v += mod();
    return v;
  }
  const Type& operator()() const { return value; }
  template <typename U>
  explicit operator U() const {
    return static_cast<U>(value);
  }
  constexpr static Type mod() { return T::value; }
  Modular& operator+=(const Modular& other) {
    if ((value += other.value) >= mod()) value -= mod();
    return *this;
  }
  Modular& operator-=(const Modular& other) {
    if ((value -= other.value) < 0) value += mod();
    return *this;
  }
  template <typename U>
  Modular& operator+=(const U& other) {
    return *this += Modular(other);
  }
  template <typename U>
  Modular& operator-=(const U& other) {
    return *this -= Modular(other);
  }
  Modular& operator++() { return *this += 1; }
  Modular& operator--() { return *this -= 1; }
  Modular operator++(int) {
    Modular result(*this);
    *this += 1;
    return result;
  }
  Modular operator--(int) {
    Modular result(*this);
    *this -= 1;
    return result;
  }
  Modular operator-() const { return Modular(-value); }
  template <typename U = T>
  typename enable_if<is_same<typename Modular<U>::Type, int>::value,
                     Modular>::type&
  operator*=(const Modular& rhs) {
    value = normalize(static_cast<int64_t>(value) *
                      static_cast<int64_t>(rhs.value));
    return *this;
  }
  template <typename U = T>
  typename enable_if<is_same<typename Modular<U>::Type, long long>::value,
                     Modular>::type&
  operator*=(const Modular& rhs) {
    long long q = static_cast<long long>(static_cast<long double>(value) *
                                         rhs.value / mod());
    value = normalize(value * rhs.value - q * mod());
    return *this;
  }
  template <typename U = T>
  typename enable_if<!is_integral<typename Modular<U>::Type>::value,
                     Modular>::type&
  operator*=(const Modular& rhs) {
    value = normalize(value * rhs.value);
    return *this;
  }
  Modular& operator/=(const Modular& other) {
    return *this *= Modular(inverse(other.value, mod()));
  }
  friend const Type& abs(const Modular& x) { return x.value; }
  template <typename U>
  friend bool operator==(const Modular<U>& lhs, const Modular<U>& rhs);
  template <typename U>
  friend bool operator<(const Modular<U>& lhs, const Modular<U>& rhs);
  template <typename V, typename U>
  friend V& operator>>(V& stream, Modular<U>& number);

 private:
  Type value;
};
template <typename T>
bool operator==(const Modular<T>& lhs, const Modular<T>& rhs) {
  return lhs.value == rhs.value;
}
template <typename T, typename U>
bool operator==(const Modular<T>& lhs, U rhs) {
  return lhs == Modular<T>(rhs);
}
template <typename T, typename U>
bool operator==(U lhs, const Modular<T>& rhs) {
  return Modular<T>(lhs) == rhs;
}
template <typename T>
bool operator!=(const Modular<T>& lhs, const Modular<T>& rhs) {
  return !(lhs == rhs);
}
template <typename T, typename U>
bool operator!=(const Modular<T>& lhs, U rhs) {
  return !(lhs == rhs);
}
template <typename T, typename U>
bool operator!=(U lhs, const Modular<T>& rhs) {
  return !(lhs == rhs);
}
template <typename T>
bool operator<(const Modular<T>& lhs, const Modular<T>& rhs) {
  return lhs.value < rhs.value;
}
template <typename T>
Modular<T> operator+(const Modular<T>& lhs, const Modular<T>& rhs) {
  return Modular<T>(lhs) += rhs;
}
template <typename T, typename U>
Modular<T> operator+(const Modular<T>& lhs, U rhs) {
  return Modular<T>(lhs) += rhs;
}
template <typename T, typename U>
Modular<T> operator+(U lhs, const Modular<T>& rhs) {
  return Modular<T>(lhs) += rhs;
}
template <typename T>
Modular<T> operator-(const Modular<T>& lhs, const Modular<T>& rhs) {
  return Modular<T>(lhs) -= rhs;
}
template <typename T, typename U>
Modular<T> operator-(const Modular<T>& lhs, U rhs) {
  return Modular<T>(lhs) -= rhs;
}
template <typename T, typename U>
Modular<T> operator-(U lhs, const Modular<T>& rhs) {
  return Modular<T>(lhs) -= rhs;
}
template <typename T>
Modular<T> operator*(const Modular<T>& lhs, const Modular<T>& rhs) {
  return Modular<T>(lhs) *= rhs;
}
template <typename T, typename U>
Modular<T> operator*(const Modular<T>& lhs, U rhs) {
  return Modular<T>(lhs) *= rhs;
}
template <typename T, typename U>
Modular<T> operator*(U lhs, const Modular<T>& rhs) {
  return Modular<T>(lhs) *= rhs;
}
template <typename T>
Modular<T> operator/(const Modular<T>& lhs, const Modular<T>& rhs) {
  return Modular<T>(lhs) /= rhs;
}
template <typename T, typename U>
Modular<T> operator/(const Modular<T>& lhs, U rhs) {
  return Modular<T>(lhs) /= rhs;
}
template <typename T, typename U>
Modular<T> operator/(U lhs, const Modular<T>& rhs) {
  return Modular<T>(lhs) /= rhs;
}
template <typename T, typename U>
Modular<T> power(const Modular<T>& a, const U& b) {
  assert(b >= 0);
  Modular<T> x = a, res = 1;
  U p = b;
  while (p > 0) {
    if (p & 1) res *= x;
    x *= x;
    p >>= 1;
  }
  return res;
}
template <typename T>
bool IsZero(const Modular<T>& number) {
  return number() == 0;
}
template <typename T>
string to_string(const Modular<T>& number) {
  return to_string(number());
}
template <typename U, typename T>
U& operator<<(U& stream, const Modular<T>& number) {
  return stream << number();
}
template <typename U, typename T>
U& operator>>(U& stream, Modular<T>& number) {
  typename common_type<typename Modular<T>::Type, long long>::type x;
  stream >> x;
  number.value = Modular<T>::normalize(x);
  return stream;
}
using ModType = int;
struct VarMod {
  static ModType value;
};
ModType VarMod::value;
ModType& md = VarMod::value;
using Mint = Modular<VarMod>;
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  int great_old_one_u, great_old_one_v;
  cin >> great_old_one_u >> great_old_one_v >> md;
  if (great_old_one_u == great_old_one_v) {
    cout << 0 << '\n';
    return 0;
  }
  Mint u = great_old_one_u;
  Mint v = great_old_one_v;
  vector<Mint> grab = {u, v};
  map<Mint, int> kill;
  kill[u] = 1;
  kill[v] = 2;
  map<Mint, Mint> dar;
  map<Mint, int> ling;
  auto Reboot = [&](Mint x) {
    vector<int> dear;
    while (dar.find(x) != dar.end()) {
      dear.push_back(ling[x]);
      x = dar[x];
    }
    reverse(dear.begin(), dear.end());
    return dear;
  };
  auto Walk_with_me = [&](Mint from, Mint to, int noose) {
    if (kill.find(to) != kill.end()) {
      if (kill[to] != kill[from]) {
        auto deal = Reboot(from);
        auto steal = Reboot(to);
        if (kill[from] == 2) {
          swap(deal, steal);
          deal.push_back(noose == 3 ? noose : 3 - noose);
        } else {
          deal.push_back(noose);
        }
        for (int roi : vector<int>(steal.rbegin(), steal.rend())) {
          deal.push_back(roi == 3 ? roi : 3 - roi);
        }
        cout << deal.size() << '\n';
        for (int i = 0; i < (int)deal.size(); i++) {
          if (i > 0) {
            cout << " ";
          }
          cout << deal[i];
        }
        cout << '\n';
        exit(0);
      }
      return;
    }
    grab.push_back(to);
    kill[to] = kill[from];
    dar[to] = from;
    ling[to] = noose;
  };
  for (int buttons = 0; buttons < (int)grab.size(); buttons++) {
    Walk_with_me(grab[buttons], grab[buttons] + 1, 1);
    Walk_with_me(grab[buttons], grab[buttons] - 1, 2);
    if (grab[buttons] != 0) {
      Walk_with_me(grab[buttons], 1 / grab[buttons], 3);
    }
  }
  cerr << "Time = " << (1.000 * clock()) / (CLOCKS_PER_SEC * 0.001) << " ms"
       << '\n';
  return 0;
}

### Prompt

In cpp, your task is to solve the following problem:

Allen is playing Number Clicker on his phone.

He starts with an integer u on the screen. Every second, he can press one of 3 buttons.

  1. Turn u → u+1 \pmod{p}. 
  2. Turn u → u+p-1 \pmod{p}. 
  3. Turn u → u^{p-2} \pmod{p}. 



Allen wants to press at most 200 buttons and end up with v on the screen. Help him!

Input

The first line of the input contains 3 positive integers: u, v, p (0 ≤ u, v ≤ p-1, 3 ≤ p ≤ 10^9 + 9). p is guaranteed to be prime.

Output

On the first line, print a single integer ℓ, the number of button presses. On the second line, print integers c_1, ..., c_ℓ, the button presses. For 1 ≤ i ≤ ℓ, 1 ≤ c_i ≤ 3.

We can show that the answer always exists.

Examples

Input

1 3 5


Output

2
1 1


Input

3 2 5


Output

1
3

Note

In the first example the integer on the screen changes as 1 → 2 → 3.

In the second example the integer on the screen changes as 3 → 2. 

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
template <typename A, typename B>
string to_string(pair<A, B> p);
template <typename A, typename B, typename C>
string to_string(tuple<A, B, C> p);
template <typename A, typename B, typename C, typename D>
string to_string(tuple<A, B, C, D> p);
string to_string(const string& s) { return '"' + s + '"'; }
string to_string(const char* s) { return to_string((string)s); }
string to_string(bool b) { return (b ? "true" : "false"); }
string to_string(vector<bool> v) {
  bool first = true;
  string res = "{";
  for (int i = 0; i < static_cast<int>(v.size()); i++) {
    if (!first) {
      res += ", ";
    }
    first = false;
    res += to_string(v[i]);
  }
  res += "}";
  return res;
}
template <size_t N>
string to_string(bitset<N> v) {
  string res = "";
  for (size_t i = 0; i < N; i++) {
    res += static_cast<char>('0' + v[i]);
  }
  return res;
}
template <typename A>
string to_string(A v) {
  bool first = true;
  string res = "{";
  for (const auto& x : v) {
    if (!first) {
      res += ", ";
    }
    first = false;
    res += to_string(x);
  }
  res += "}";
  return res;
}
template <typename A, typename B>
string to_string(pair<A, B> p) {
  return "(" + to_string(p.first) + ", " + to_string(p.second) + ")";
}
template <typename A, typename B, typename C>
string to_string(tuple<A, B, C> p) {
  return "(" + to_string(get<0>(p)) + ", " + to_string(get<1>(p)) + ", " +
         to_string(get<2>(p)) + ")";
}
template <typename A, typename B, typename C, typename D>
string to_string(tuple<A, B, C, D> p) {
  return "(" + to_string(get<0>(p)) + ", " + to_string(get<1>(p)) + ", " +
         to_string(get<2>(p)) + ", " + to_string(get<3>(p)) + ")";
}
void debug_out() { cerr << endl; }
template <typename Head, typename... Tail>
void debug_out(Head H, Tail... T) {
  cerr << " " << to_string(H);
  debug_out(T...);
}
template <typename T>
T inverse(T a, T m) {
  T u = 0, v = 1;
  while (a != 0) {
    T t = m / a;
    m -= t * a;
    swap(a, m);
    u -= t * v;
    swap(u, v);
  }
  assert(m == 1);
  return u;
}
template <typename T>
class Modular {
 public:
  using Type = typename decay<decltype(T::value)>::type;
  constexpr Modular() : value() {}
  template <typename U>
  Modular(const U& x) {
    value = normalize(x);
  }
  template <typename U>
  static Type normalize(const U& x) {
    Type v;
    if (-mod() <= x && x < mod())
      v = static_cast<Type>(x);
    else
      v = static_cast<Type>(x % mod());
    if (v < 0) v += mod();
    return v;
  }
  const Type& operator()() const { return value; }
  template <typename U>
  explicit operator U() const {
    return static_cast<U>(value);
  }
  constexpr static Type mod() { return T::value; }
  Modular& operator+=(const Modular& other) {
    if ((value += other.value) >= mod()) value -= mod();
    return *this;
  }
  Modular& operator-=(const Modular& other) {
    if ((value -= other.value) < 0) value += mod();
    return *this;
  }
  template <typename U>
  Modular& operator+=(const U& other) {
    return *this += Modular(other);
  }
  template <typename U>
  Modular& operator-=(const U& other) {
    return *this -= Modular(other);
  }
  Modular& operator++() { return *this += 1; }
  Modular& operator--() { return *this -= 1; }
  Modular operator++(int) {
    Modular result(*this);
    *this += 1;
    return result;
  }
  Modular operator--(int) {
    Modular result(*this);
    *this -= 1;
    return result;
  }
  Modular operator-() const { return Modular(-value); }
  template <typename U = T>
  typename enable_if<is_same<typename Modular<U>::Type, int>::value,
                     Modular>::type&
  operator*=(const Modular& rhs) {
    value = normalize(static_cast<int64_t>(value) *
                      static_cast<int64_t>(rhs.value));
    return *this;
  }
  template <typename U = T>
  typename enable_if<is_same<typename Modular<U>::Type, long long>::value,
                     Modular>::type&
  operator*=(const Modular& rhs) {
    long long q = static_cast<long long>(static_cast<long double>(value) *
                                         rhs.value / mod());
    value = normalize(value * rhs.value - q * mod());
    return *this;
  }
  template <typename U = T>
  typename enable_if<!is_integral<typename Modular<U>::Type>::value,
                     Modular>::type&
  operator*=(const Modular& rhs) {
    value = normalize(value * rhs.value);
    return *this;
  }
  Modular& operator/=(const Modular& other) {
    return *this *= Modular(inverse(other.value, mod()));
  }
  friend const Type& abs(const Modular& x) { return x.value; }
  template <typename U>
  friend bool operator==(const Modular<U>& lhs, const Modular<U>& rhs);
  template <typename U>
  friend bool operator<(const Modular<U>& lhs, const Modular<U>& rhs);
  template <typename V, typename U>
  friend V& operator>>(V& stream, Modular<U>& number);

 private:
  Type value;
};
template <typename T>
bool operator==(const Modular<T>& lhs, const Modular<T>& rhs) {
  return lhs.value == rhs.value;
}
template <typename T, typename U>
bool operator==(const Modular<T>& lhs, U rhs) {
  return lhs == Modular<T>(rhs);
}
template <typename T, typename U>
bool operator==(U lhs, const Modular<T>& rhs) {
  return Modular<T>(lhs) == rhs;
}
template <typename T>
bool operator!=(const Modular<T>& lhs, const Modular<T>& rhs) {
  return !(lhs == rhs);
}
template <typename T, typename U>
bool operator!=(const Modular<T>& lhs, U rhs) {
  return !(lhs == rhs);
}
template <typename T, typename U>
bool operator!=(U lhs, const Modular<T>& rhs) {
  return !(lhs == rhs);
}
template <typename T>
bool operator<(const Modular<T>& lhs, const Modular<T>& rhs) {
  return lhs.value < rhs.value;
}
template <typename T>
Modular<T> operator+(const Modular<T>& lhs, const Modular<T>& rhs) {
  return Modular<T>(lhs) += rhs;
}
template <typename T, typename U>
Modular<T> operator+(const Modular<T>& lhs, U rhs) {
  return Modular<T>(lhs) += rhs;
}
template <typename T, typename U>
Modular<T> operator+(U lhs, const Modular<T>& rhs) {
  return Modular<T>(lhs) += rhs;
}
template <typename T>
Modular<T> operator-(const Modular<T>& lhs, const Modular<T>& rhs) {
  return Modular<T>(lhs) -= rhs;
}
template <typename T, typename U>
Modular<T> operator-(const Modular<T>& lhs, U rhs) {
  return Modular<T>(lhs) -= rhs;
}
template <typename T, typename U>
Modular<T> operator-(U lhs, const Modular<T>& rhs) {
  return Modular<T>(lhs) -= rhs;
}
template <typename T>
Modular<T> operator*(const Modular<T>& lhs, const Modular<T>& rhs) {
  return Modular<T>(lhs) *= rhs;
}
template <typename T, typename U>
Modular<T> operator*(const Modular<T>& lhs, U rhs) {
  return Modular<T>(lhs) *= rhs;
}
template <typename T, typename U>
Modular<T> operator*(U lhs, const Modular<T>& rhs) {
  return Modular<T>(lhs) *= rhs;
}
template <typename T>
Modular<T> operator/(const Modular<T>& lhs, const Modular<T>& rhs) {
  return Modular<T>(lhs) /= rhs;
}
template <typename T, typename U>
Modular<T> operator/(const Modular<T>& lhs, U rhs) {
  return Modular<T>(lhs) /= rhs;
}
template <typename T, typename U>
Modular<T> operator/(U lhs, const Modular<T>& rhs) {
  return Modular<T>(lhs) /= rhs;
}
template <typename T, typename U>
Modular<T> power(const Modular<T>& a, const U& b) {
  assert(b >= 0);
  Modular<T> x = a, res = 1;
  U p = b;
  while (p > 0) {
    if (p & 1) res *= x;
    x *= x;
    p >>= 1;
  }
  return res;
}
template <typename T>
bool IsZero(const Modular<T>& number) {
  return number() == 0;
}
template <typename T>
string to_string(const Modular<T>& number) {
  return to_string(number());
}
template <typename U, typename T>
U& operator<<(U& stream, const Modular<T>& number) {
  return stream << number();
}
template <typename U, typename T>
U& operator>>(U& stream, Modular<T>& number) {
  typename common_type<typename Modular<T>::Type, long long>::type x;
  stream >> x;
  number.value = Modular<T>::normalize(x);
  return stream;
}
using ModType = int;
struct VarMod {
  static ModType value;
};
ModType VarMod::value;
ModType& md = VarMod::value;
using Mint = Modular<VarMod>;
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  int great_old_one_u, great_old_one_v;
  cin >> great_old_one_u >> great_old_one_v >> md;
  if (great_old_one_u == great_old_one_v) {
    cout << 0 << '\n';
    return 0;
  }
  Mint u = great_old_one_u;
  Mint v = great_old_one_v;
  vector<Mint> grab = {u, v};
  map<Mint, int> kill;
  kill[u] = 1;
  kill[v] = 2;
  map<Mint, Mint> dar;
  map<Mint, int> ling;
  auto Reboot = [&](Mint x) {
    vector<int> dear;
    while (dar.find(x) != dar.end()) {
      dear.push_back(ling[x]);
      x = dar[x];
    }
    reverse(dear.begin(), dear.end());
    return dear;
  };
  auto Walk_with_me = [&](Mint from, Mint to, int noose) {
    if (kill.find(to) != kill.end()) {
      if (kill[to] != kill[from]) {
        auto deal = Reboot(from);
        auto steal = Reboot(to);
        if (kill[from] == 2) {
          swap(deal, steal);
          deal.push_back(noose == 3 ? noose : 3 - noose);
        } else {
          deal.push_back(noose);
        }
        for (int roi : vector<int>(steal.rbegin(), steal.rend())) {
          deal.push_back(roi == 3 ? roi : 3 - roi);
        }
        cout << deal.size() << '\n';
        for (int i = 0; i < (int)deal.size(); i++) {
          if (i > 0) {
            cout << " ";
          }
          cout << deal[i];
        }
        cout << '\n';
        exit(0);
      }
      return;
    }
    grab.push_back(to);
    kill[to] = kill[from];
    dar[to] = from;
    ling[to] = noose;
  };
  for (int buttons = 0; buttons < (int)grab.size(); buttons++) {
    Walk_with_me(grab[buttons], grab[buttons] + 1, 1);
    Walk_with_me(grab[buttons], grab[buttons] - 1, 2);
    if (grab[buttons] != 0) {
      Walk_with_me(grab[buttons], 1 / grab[buttons], 3);
    }
  }
  cerr << "Time = " << (1.000 * clock()) / (CLOCKS_PER_SEC * 0.001) << " ms"
       << '\n';
  return 0;
}

```