#include <bits/stdc++.h>
template <typename T>
void MACRO_VAR_Scan(T& t) {
  std::cin >> t;
}
template <typename First, typename... Rest>
void MACRO_VAR_Scan(First& first, Rest&... rest) {
  std::cin >> first;
  MACRO_VAR_Scan(rest...);
}
template <typename T>
void MACRO_VEC_ROW_Init(int n, T& t) {
  t.resize(n);
}
template <typename First, typename... Rest>
void MACRO_VEC_ROW_Init(int n, First& first, Rest&... rest) {
  first.resize(n);
  MACRO_VEC_ROW_Init(n, rest...);
}
template <typename T>
void MACRO_VEC_ROW_Scan(int p, T& t) {
  std::cin >> t[p];
}
template <typename First, typename... Rest>
void MACRO_VEC_ROW_Scan(int p, First& first, Rest&... rest) {
  std::cin >> first[p];
  MACRO_VEC_ROW_Scan(p, rest...);
}
template <typename T>
inline T CHMAX(T& a, const T b) {
  return a = (a < b) ? b : a;
}
template <typename T>
inline T CHMIN(T& a, const T b) {
  return a = (a > b) ? b : a;
}
void CHECKTIME(std::function<void()> f) {
  auto start = std::chrono::system_clock::now();
  f();
  auto end = std::chrono::system_clock::now();
  auto res = std::chrono::duration_cast<std::chrono::nanoseconds>((end - start))
                 .count();
  std::cerr << "[Time:" << res << "ns  (" << res / (1.0e9) << "s)]\n";
}
template <class T>
std::vector<std::vector<T>> VV(int n, int m, T init = T()) {
  return std::vector<std::vector<T>>(n, std::vector<T>(m, init));
}
template <typename S, typename T>
std::ostream& operator<<(std::ostream& os, std::pair<S, T> p) {
  os << "(" << p.first << ", " << p.second << ")";
  return os;
}
using ll = long long;
using ull = unsigned long long;
using ld = long double;
using PAIR = std::pair<ll, ll>;
using PAIRLL = std::pair<ll, ll>;
constexpr ll INFINT = 1 << 30;
constexpr ll INFINT_LIM = (1LL << 31) - 1;
constexpr ll INFLL = 1LL << 60;
constexpr ll INFLL_LIM = (1LL << 62) - 1 + (1LL << 62);
constexpr double EPS = 1e-9;
constexpr ll MOD = 1000000007;
constexpr double PI = 3.141592653589793238462643383279;
template <class T>
struct CVECTOR {
  std::vector<T> cumsum;
  CVECTOR(const std::vector<T>& a) : cumsum(a.size() + 1, 0) {
    for (size_t i = 0; i < a.size(); ++i) cumsum[i + 1] = cumsum[i] + a[i];
  }
  T operator[](ll idx) { return cumsum[idx + 1]; }
};
template <class T>
CVECTOR<T> make_cvector(const std::vector<T>& a) {
  return CVECTOR<T>(a);
}
ll powMod(ll n, ll p, ll mod) {
  ll res = 1;
  while (p) {
    if (p & 1) res *= n, res %= mod;
    n *= n, n %= mod;
    p >>= 1;
  }
  return res;
}
std::map<ll, ll> inv;
ll invMod(ll n, ll mod) {
  if (inv.find(n) != inv.end()) return inv[n];
  return inv[n] = powMod(n, mod - 2, mod);
}
signed main() {
  std::ios::sync_with_stdio(false);
  std::cin.tie(0);
  ;
  ll a, b, p, x;
  MACRO_VAR_Scan(a, b, p, x);
  ;
  std::vector<ll> v(p);
  for (ll n = (1); n < (p); ++n) {
    v[n] = b * invMod(powMod(a, n, p), p) % p;
  }
  ll ans = 0;
  {
    ll t = x / (p * (p - 1));
    ans += t * (p - 1);
    x -= t * p * (p - 1);
  }
  ll q = x / (p - 1), r = x % (p - 1);
  for (ll i = (1); i < (p); ++i) {
    ll num = q + (i <= r);
    if ((i - num + 1 <= v[i] && v[i] < i + 1)) ++ans;
    if ((i - num + 1 + p <= v[i] && v[i] < p)) ++ans;
  }
  std::cout << (ans);
  std::cout << "\n";
  ;
  return 0;
}

### Prompt

Your task is to create a cpp solution to the following problem:

Given an integer x. Your task is to find out how many positive integers n (1 ≤ n ≤ x) satisfy $$$n ⋅ a^n ≡ b   (mod\;p), where a, b, p$$$ are all known constants.

Input

The only line contains four integers a,b,p,x (2 ≤ p ≤ 10^6+3, 1 ≤ a,b < p, 1 ≤ x ≤ 10^{12}). It is guaranteed that p is a prime.

Output

Print a single integer: the number of possible answers n.

Examples

Input

2 3 5 8


Output

2


Input

4 6 7 13


Output

1


Input

233 233 10007 1


Output

1

Note

In the first sample, we can see that n=2 and n=8 are possible answers.

### Response

```cpp
#include <bits/stdc++.h>
template <typename T>
void MACRO_VAR_Scan(T& t) {
  std::cin >> t;
}
template <typename First, typename... Rest>
void MACRO_VAR_Scan(First& first, Rest&... rest) {
  std::cin >> first;
  MACRO_VAR_Scan(rest...);
}
template <typename T>
void MACRO_VEC_ROW_Init(int n, T& t) {
  t.resize(n);
}
template <typename First, typename... Rest>
void MACRO_VEC_ROW_Init(int n, First& first, Rest&... rest) {
  first.resize(n);
  MACRO_VEC_ROW_Init(n, rest...);
}
template <typename T>
void MACRO_VEC_ROW_Scan(int p, T& t) {
  std::cin >> t[p];
}
template <typename First, typename... Rest>
void MACRO_VEC_ROW_Scan(int p, First& first, Rest&... rest) {
  std::cin >> first[p];
  MACRO_VEC_ROW_Scan(p, rest...);
}
template <typename T>
inline T CHMAX(T& a, const T b) {
  return a = (a < b) ? b : a;
}
template <typename T>
inline T CHMIN(T& a, const T b) {
  return a = (a > b) ? b : a;
}
void CHECKTIME(std::function<void()> f) {
  auto start = std::chrono::system_clock::now();
  f();
  auto end = std::chrono::system_clock::now();
  auto res = std::chrono::duration_cast<std::chrono::nanoseconds>((end - start))
                 .count();
  std::cerr << "[Time:" << res << "ns  (" << res / (1.0e9) << "s)]\n";
}
template <class T>
std::vector<std::vector<T>> VV(int n, int m, T init = T()) {
  return std::vector<std::vector<T>>(n, std::vector<T>(m, init));
}
template <typename S, typename T>
std::ostream& operator<<(std::ostream& os, std::pair<S, T> p) {
  os << "(" << p.first << ", " << p.second << ")";
  return os;
}
using ll = long long;
using ull = unsigned long long;
using ld = long double;
using PAIR = std::pair<ll, ll>;
using PAIRLL = std::pair<ll, ll>;
constexpr ll INFINT = 1 << 30;
constexpr ll INFINT_LIM = (1LL << 31) - 1;
constexpr ll INFLL = 1LL << 60;
constexpr ll INFLL_LIM = (1LL << 62) - 1 + (1LL << 62);
constexpr double EPS = 1e-9;
constexpr ll MOD = 1000000007;
constexpr double PI = 3.141592653589793238462643383279;
template <class T>
struct CVECTOR {
  std::vector<T> cumsum;
  CVECTOR(const std::vector<T>& a) : cumsum(a.size() + 1, 0) {
    for (size_t i = 0; i < a.size(); ++i) cumsum[i + 1] = cumsum[i] + a[i];
  }
  T operator[](ll idx) { return cumsum[idx + 1]; }
};
template <class T>
CVECTOR<T> make_cvector(const std::vector<T>& a) {
  return CVECTOR<T>(a);
}
ll powMod(ll n, ll p, ll mod) {
  ll res = 1;
  while (p) {
    if (p & 1) res *= n, res %= mod;
    n *= n, n %= mod;
    p >>= 1;
  }
  return res;
}
std::map<ll, ll> inv;
ll invMod(ll n, ll mod) {
  if (inv.find(n) != inv.end()) return inv[n];
  return inv[n] = powMod(n, mod - 2, mod);
}
signed main() {
  std::ios::sync_with_stdio(false);
  std::cin.tie(0);
  ;
  ll a, b, p, x;
  MACRO_VAR_Scan(a, b, p, x);
  ;
  std::vector<ll> v(p);
  for (ll n = (1); n < (p); ++n) {
    v[n] = b * invMod(powMod(a, n, p), p) % p;
  }
  ll ans = 0;
  {
    ll t = x / (p * (p - 1));
    ans += t * (p - 1);
    x -= t * p * (p - 1);
  }
  ll q = x / (p - 1), r = x % (p - 1);
  for (ll i = (1); i < (p); ++i) {
    ll num = q + (i <= r);
    if ((i - num + 1 <= v[i] && v[i] < i + 1)) ++ans;
    if ((i - num + 1 + p <= v[i] && v[i] < p)) ++ans;
  }
  std::cout << (ans);
  std::cout << "\n";
  ;
  return 0;
}

```