Problem p03810 (C++)

Buggy submission (status: Runtime Error):
#include <bits/stdc++.h>
#pragma GCC diagnostic ignored "-Wsign-compare"
#pragma GCC diagnostic ignored "-Wsign-conversion"
#define NDEBUG
#define SHOW(...) static_cast<void>(0)
//!===========================================================!//
//!  dP     dP                          dP                    !//
//!  88     88                          88                    !//
//!  88aaaaa88a .d8888b. .d8888b. .d888b88 .d8888b. 88d888b.  !//
//!  88     88  88ooood8 88'  '88 88'  '88 88ooood8 88'  '88  !//
//!  88     88  88.  ... 88.  .88 88.  .88 88.  ... 88        !//
//!  dP     dP  '88888P' '88888P8 '88888P8 '88888P' dP        !//
//!===========================================================!//
template <typename T, typename A>
std::istream &operator>>(std::istream &is, std::vector<T, A> &v) {
  for (auto &e : v) {
    is >> e;
  }
  return is;
}
using ld = long double;
using uint = unsigned int;
using ll = long long;
using ull = unsigned long long;
constexpr unsigned int MOD = 1000000007;
template <typename T> constexpr T INF = std::numeric_limits<T>::max() / 4;
template <typename F> constexpr F PI = static_cast<F>(3.1415926535897932385);
std::mt19937 mt{std::random_device{}()};
template <typename T> bool chmin(T &a, const T &b) {
  return a = std::min(a, b), a == b;
}
template <typename T> bool chmax(T &a, const T &b) {
  return a = std::max(a, b), a == b;
}
template <typename T> std::vector<T> Vec(const std::size_t n, T v) {
  return std::vector<T>(n, v);
}
template <class... Args> auto Vec(const std::size_t n, Args... args) {
  return std::vector<decltype(Vec(args...))>(n, Vec(args...));
}
template <typename T> constexpr T popCount(const T u) {
#ifdef __has_builtin
  return u == 0 ? T(0) : (T)__builtin_popcountll(u);
#else
  unsigned long long v = static_cast<unsigned long long>(u);
  return v = (v & 0x5555555555555555ULL) + (v >> 1 & 0x5555555555555555ULL),
         v = (v & 0x3333333333333333ULL) + (v >> 2 & 0x3333333333333333ULL),
         v = (v + (v >> 4)) & 0x0F0F0F0F0F0F0F0FULL,
         static_cast<T>(v * 0x0101010101010101ULL >> 56 & 0x7f);
#endif
}
template <typename T> constexpr T log2p1(const T u) {
#ifdef __has_builtin
  return u == 0 ? T(0) : T(64 - __builtin_clzll(u));
#else
  unsigned long long v = static_cast<unsigned long long>(u);
  return v = static_cast<unsigned long long>(v), v |= (v >> 1), v |= (v >> 2),
         v |= (v >> 4), v |= (v >> 8), v |= (v >> 16), v |= (v >> 32),
         popCount(v);
#endif
}
template <typename T> constexpr T clog(const T v) {
  return v == 0 ? T(0) : log2p1(v - 1);
}
template <typename T> constexpr T msbp1(const T v) { return log2p1(v); }
template <typename T> constexpr T lsbp1(const T v) {
#ifdef __has_builtin
  return __builtin_ffsll(v);
#else
  return v == 0 ? T(0) : popCount((v & (-v)) - T(1)) + T(1);
#endif
}
template <typename T> constexpr bool ispow2(const T v) {
  return popCount(v) == 1;
}
template <typename T> constexpr T ceil2(const T v) {
  return v == 0 ? T(1) : T(1) << log2p1(v - 1);
}
template <typename T> constexpr T floor2(const T v) {
  return v == 0 ? T(0) : T(1) << (log2p1(v) - 1);
}
//!====================================================================================!//
//!    .88888.   a88888b. 888888ba        d88b       dP         a88888b.
//!    8888ba.88ba   !//
//!   d8'   '88 d8'   '88 88    '8b       8''8       88        d8'   '88 88  '8b
//!   '8b  !// 88        88        88     88       d8b        88        88 88 88
//!   88  !// 88   YP88 88        88     88     d8P'8b       88        88 88 88
//!   88  !// Y8.   .88 Y8.   .88 88    .8P     d8' '8bP     88        Y8.   .88
//!   88   88   88  !//
//!    '88888'   Y88888P' 8888888P      '888P''YP    88888888P  Y88888P' dP   dP
//!    dP  !//
//!====================================================================================!//
template <typename T> constexpr T gcd(const T a, const T b) {
  return (b != (T)0) ? gcd(b, a % b) : a;
}
template <typename T> constexpr T lcm(const T a, const T b) {
  return (a == (T)0 and b == (T)0) ? (T)0 : (a / gcd(a, b)) * b;
}
//!============================================!//
//!    8888ba.88ba             oo              !//
//!    88  '8b  '8b                            !//
//!    88   88   88  .d8888b.  dP  88d888b.    !//
//!    88   88   88  88'  '88  88  88'  '88    !//
//!    88   88   88  88.  .88  88  88    88    !//
//!    dP   dP   dP  '88888P8  dP  dP    dP    !//
//!============================================!//
int main() {
  int N;
  std::cin >> N;
  std::vector<ll> A(N);
  std::cin >> A;
  auto ok = [&, N](auto &&self, std::vector<ll> &A) {
    int even = 0;
    for (int i = 0; i < N; i++) {
      even += (A[i] % 2 == 0 ? 1 : 0);
    }
    const int odd = N - even;
    if (even % 2 == 1) {
      return true;
    } else if (odd >= 2) {
      return false;
    } else {
      ll g = 0;
      for (int i = 0; i < N; i++) {
        if (A[i] % 2 == 1) {
          A[i]--;
        }
        g = gcd(g, A[i]);
      }
      for (int i = 0; i < N; i++) {
        A[i] /= g;
      }
      return not self(self, A);
    }
  };
  std::cout << (ok(ok, A) ? "First" : "Second") << std::endl;
  return 0;
}


Fixed submission:
#include <bits/stdc++.h>
#pragma GCC diagnostic ignored "-Wsign-compare"
#pragma GCC diagnostic ignored "-Wsign-conversion"
#define NDEBUG
#define SHOW(...) static_cast<void>(0)
//!===========================================================!//
//!  dP     dP                          dP                    !//
//!  88     88                          88                    !//
//!  88aaaaa88a .d8888b. .d8888b. .d888b88 .d8888b. 88d888b.  !//
//!  88     88  88ooood8 88'  '88 88'  '88 88ooood8 88'  '88  !//
//!  88     88  88.  ... 88.  .88 88.  .88 88.  ... 88        !//
//!  dP     dP  '88888P' '88888P8 '88888P8 '88888P' dP        !//
//!===========================================================!//
template <typename T, typename A>
std::istream &operator>>(std::istream &is, std::vector<T, A> &v) {
  for (auto &e : v) {
    is >> e;
  }
  return is;
}
using ld = long double;
using uint = unsigned int;
using ll = long long;
using ull = unsigned long long;
constexpr unsigned int MOD = 1000000007;
template <typename T> constexpr T INF = std::numeric_limits<T>::max() / 4;
template <typename F> constexpr F PI = static_cast<F>(3.1415926535897932385);
std::mt19937 mt{std::random_device{}()};
template <typename T> bool chmin(T &a, const T &b) {
  return a = std::min(a, b), a == b;
}
template <typename T> bool chmax(T &a, const T &b) {
  return a = std::max(a, b), a == b;
}
template <typename T> std::vector<T> Vec(const std::size_t n, T v) {
  return std::vector<T>(n, v);
}
template <class... Args> auto Vec(const std::size_t n, Args... args) {
  return std::vector<decltype(Vec(args...))>(n, Vec(args...));
}
template <typename T> constexpr T popCount(const T u) {
#ifdef __has_builtin
  return u == 0 ? T(0) : (T)__builtin_popcountll(u);
#else
  unsigned long long v = static_cast<unsigned long long>(u);
  return v = (v & 0x5555555555555555ULL) + (v >> 1 & 0x5555555555555555ULL),
         v = (v & 0x3333333333333333ULL) + (v >> 2 & 0x3333333333333333ULL),
         v = (v + (v >> 4)) & 0x0F0F0F0F0F0F0F0FULL,
         static_cast<T>(v * 0x0101010101010101ULL >> 56 & 0x7f);
#endif
}
template <typename T> constexpr T log2p1(const T u) {
#ifdef __has_builtin
  return u == 0 ? T(0) : T(64 - __builtin_clzll(u));
#else
  unsigned long long v = static_cast<unsigned long long>(u);
  return v = static_cast<unsigned long long>(v), v |= (v >> 1), v |= (v >> 2),
         v |= (v >> 4), v |= (v >> 8), v |= (v >> 16), v |= (v >> 32),
         popCount(v);
#endif
}
template <typename T> constexpr T clog(const T v) {
  return v == 0 ? T(0) : log2p1(v - 1);
}
template <typename T> constexpr T msbp1(const T v) { return log2p1(v); }
template <typename T> constexpr T lsbp1(const T v) {
#ifdef __has_builtin
  return __builtin_ffsll(v);
#else
  return v == 0 ? T(0) : popCount((v & (-v)) - T(1)) + T(1);
#endif
}
template <typename T> constexpr bool ispow2(const T v) {
  return popCount(v) == 1;
}
template <typename T> constexpr T ceil2(const T v) {
  return v == 0 ? T(1) : T(1) << log2p1(v - 1);
}
template <typename T> constexpr T floor2(const T v) {
  return v == 0 ? T(0) : T(1) << (log2p1(v) - 1);
}
//!====================================================================================!//
//!    .88888.   a88888b. 888888ba        d88b       dP         a88888b.
//!    8888ba.88ba   !//
//!   d8'   '88 d8'   '88 88    '8b       8''8       88        d8'   '88 88  '8b
//!   '8b  !// 88        88        88     88       d8b        88        88 88 88
//!   88  !// 88   YP88 88        88     88     d8P'8b       88        88 88 88
//!   88  !// Y8.   .88 Y8.   .88 88    .8P     d8' '8bP     88        Y8.   .88
//!   88   88   88  !//
//!    '88888'   Y88888P' 8888888P      '888P''YP    88888888P  Y88888P' dP   dP
//!    dP  !//
//!====================================================================================!//
template <typename T> constexpr T gcd(const T a, const T b) {
  return (b != (T)0) ? gcd(b, a % b) : a;
}
template <typename T> constexpr T lcm(const T a, const T b) {
  return (a == (T)0 and b == (T)0) ? (T)0 : (a / gcd(a, b)) * b;
}
//!============================================!//
//!    8888ba.88ba             oo              !//
//!    88  '8b  '8b                            !//
//!    88   88   88  .d8888b.  dP  88d888b.    !//
//!    88   88   88  88'  '88  88  88'  '88    !//
//!    88   88   88  88.  .88  88  88    88    !//
//!    dP   dP   dP  '88888P8  dP  dP    dP    !//
//!============================================!//
int main() {
  int N;
  std::cin >> N;
  std::vector<ll> A(N);
  std::cin >> A;
  auto ok = [&, N](auto &&self, std::vector<ll> &A) {
    bool o = false;
    for (int i = 0; i < N; i++) {
      o |= A[i] == 1;
    }
    if (o) {
      const ll S = std::accumulate(A.begin(), A.end(), 0LL) - N;
      return S % 2 == 1;
    }
    int even = 0;
    for (int i = 0; i < N; i++) {
      even += (A[i] % 2 == 0 ? 1 : 0);
    }
    const int odd = N - even;
    if (even % 2 == 1) {
      return true;
    } else if (odd >= 2) {
      return false;
    } else {
      ll g = 0;
      for (int i = 0; i < N; i++) {
        if (A[i] % 2 == 1) {
          A[i]--;
        }
        g = gcd(g, A[i]);
      }
      for (int i = 0; i < N; i++) {
        A[i] /= g;
      }
      return not self(self, A);
    }
  };
  std::cout << (ok(ok, A) ? "First" : "Second") << std::endl;
  return 0;
}