#1003567 (C++17) No.2847 Birthday Attack

• 問題: No.2847 Birthday Attack
• ユーザー: Aging1986
• 提出日時: 2024-08-23 23:47:58
• 言語: C++17 (gcc 12.3.0 + boost 1.83.0)
• 結果: AC
• 実行時間: 219 ms / 3,000 ms
• コード長: 10,605 bytes
• コンパイル時間: 2,345 ms
• コンパイル使用メモリ: 209,604 KB
• 実行使用メモリ: 6,944 KB
• 最終ジャッジ日時: 2024-08-23 23:48:03
• 合計ジャッジ時間: 4,891 ms
• ジャッジサーバーID （参考情報）: judge3 / judge1

入力	結果	実行時間; 実行使用メモリ
testcase_00	AC	2 ms; 6,812 KB
testcase_01	AC	2 ms; 6,944 KB
testcase_02	AC	2 ms; 6,940 KB
testcase_03	AC	5 ms; 6,940 KB
testcase_04	AC	2 ms; 6,940 KB
testcase_05	AC	219 ms; 6,940 KB
testcase_06	AC	114 ms; 6,940 KB
testcase_07	AC	187 ms; 6,944 KB
testcase_08	AC	51 ms; 6,940 KB
testcase_09	AC	116 ms; 6,940 KB
testcase_10	AC	71 ms; 6,944 KB
testcase_11	AC	33 ms; 6,940 KB
testcase_12	AC	175 ms; 6,944 KB
testcase_13	AC	187 ms; 6,940 KB
testcase_14	AC	136 ms; 6,944 KB
testcase_15	AC	91 ms; 6,944 KB
testcase_16	AC	99 ms; 6,944 KB
testcase_17	AC	72 ms; 6,940 KB

ソースコード

#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef pair<ll, ll> pll;
typedef pair<int, int> pii;
typedef pair<double, double> pdd;
typedef vector<int> vi;
typedef vector<ll> vll;
typedef vector<double> vd;
typedef vector<string> vs;
typedef vector<vi> vvi;
typedef vector<vvi> vvvi;
typedef vector<vll> vvll;
typedef vector<vvll> vvvll;
typedef vector<pii> vpii;
typedef vector<vpii> vvpii;
typedef vector<pll> vpll;
typedef vector<vpll> vvpll;
typedef vector<pdd> vpdd;
typedef vector<vd> vvd;
#define yn(ans) printf("%s\n", (ans)?"Yes":"No");
#define YN(ans) printf("%s\n", (ans)?"YES":"NO");
    template<class T> bool chmax(T &a, T b) {
	if (a >= b) return false;
	a = b; return true;
}
template<class T> bool chmin(T &a, T b) {
	if (a <= b) return false;
	a = b; return true;
}
#define FOR(i, s, e, t) for ((i) = (s); (i) < (e); (i) += (t)) 
#define REP(i, e) for (int i = 0; i < (e); ++i) 
#define REP1(i, s, e) for (int i = (s); i < (e); ++i)
#define RREP(i, e) for (int i = (e); i >= 0; --i)
#define RREP1(i, e, s) for (int i = (e); i >= (s); --i)
#define all(v) v.begin(), v.end()
#define pb push_back
#define qb pop_back
#define pf push_front
#define qf pop_front
#define maxe max_element
#define mine min_element
ll inf = 1e18;
#define DEBUG printf("%d\n", __LINE__); fflush(stdout);
template<class T> void print(vector<T> &v, bool withSize = false) {
	if (withSize) cout << v.size() << endl;
	REP(i, v.size()) cout << v[i] << " "; 
	cout << endl;
}
mt19937_64 rng((unsigned int) chrono::steady_clock::now().time_since_epoch().count());

int __FAST_IO__ = []() {
	std::ios::sync_with_stdio(0);
	std::cin.tie(0);
	std::cout.tie(0);
	return 0;
}();

// Mint & Combinatorics
 
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);
  }
  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) {
#ifdef _WIN32
    uint64_t x = static_cast<int64_t>(value) * static_cast<int64_t>(rhs.value);
    uint32_t xh = static_cast<uint32_t>(x >> 32), xl = static_cast<uint32_t>(x), d, m;
    asm(
      "divl %4; \n\t"
      : "=a" (d), "=d" (m)
      : "d" (xh), "a" (xl), "r" (mod())
    );
    value = m;
#else
    value = normalize(static_cast<int64_t>(value) * static_cast<int64_t>(rhs.value));
#endif
    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());
}
 
// U == std::ostream? but done this way because of fastoutput
template <typename U, typename T>
U& operator<<(U& stream, const Modular<T>& number) {
  return stream << number();
}
 
// U == std::istream? but done this way because of fastinput
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;
}
 
struct MOD {
    static int value;
};
int MOD::value = 998244353;
using Mint = Modular<MOD>;
typedef vector<Mint> vm;
typedef vector<vm> vvm;
typedef vector<vvm> vvvm;

vector<Mint> fac, ifac;
void initFac(int N) {
	fac.resize(N + 1);
	ifac.resize(N + 1);
	fac[0] = ifac[0] = 1;
	REP1(i, 1, N + 1) {
		fac[i] = fac[i - 1] * i;
	}
	ifac[N] = 1 / fac[N];
	RREP1(i, N - 1, 1) {
		ifac[i] = (i + 1) * ifac[i + 1];
	}
}
 
Mint C(int m, int n) {
	if (m < n || n < 0) return 0;
	return fac[m] * ifac[n] * ifac[m - n]; 
}

Mint P(int m, int n) {
	if (m < n || n < 0) return 0;
	return fac[m] * ifac[m - n];
}



#define TESTS int t; cin >> t; while (t--)
#define TEST 
int main() {
    TEST {
    	int X, Y, M;
    	cin >> X >> Y >> M;
    	MOD::value = M;
    	
    	Mint ans = 0;
        
        for (int r = 1; 2 * r + 1 <= X; ++r) {
            ans += 2ll * (X - 2 * r) * Y;
        } 
        for (int r = 1; 2 * r + 1 <= Y; ++r) {
            ans += 2ll * (Y - 2 * r) * X;
        }
        
        for (int n = 1; 4 * n + 2 <= X; ++n) {
            for (int m = n + 1; ; m += 2) {
                if (__gcd(m, n) > 1) continue;
                ll a = 2ll * m * m - 2ll * n * n, b = 4ll * m * n;
                if (a + 1 > X || b + 1 > Y) break;
                ll d = min((X - 1) / a, (Y - 1) / b);
                ll e = (d * (d + 1) / 2) % M;
                ll f = ((__int128_t)d * (d + 1) * (2 * d + 1) / 6) % M;
                Mint cur = 0;
                cur += Mint(1) * X * Y * d;
                cur -= Mint(e) * X * b;
                cur -= Mint(e) * Y * a;
                cur += Mint(f) * a * b;
               // printf("add %lld %lld %d %d %d\n", a / 2, b / 2, n, m, 4 * cur);
                ans += 4 * cur;
            }
        }
        for (int n = 1; 4 * n + 2 <= Y; ++n) {
            for (int m = n + 1; ; m += 2) {
                if (__gcd(m, n) > 1) continue;
                ll a = 2ll * m * m - 2ll * n * n, b = 4ll * m * n;
                if (a + 1 > Y || b + 1 > X) break;
                if (a == b) continue;
                ll d = min((X - 1) / b, (Y - 1) / a);
                ll e = (d * (d + 1) / 2) % M;
                ll f = ((__int128_t)d * (d + 1) * (2 * d + 1) / 6) % M;
                Mint cur = 0;
                cur += Mint(1) * X * Y * d;
                cur -= Mint(e) * X * a;
                cur -= Mint(e) * Y * b;
                cur += Mint(f) * a * b;
               // printf("add %lld %lld %d %d %d\n", a / 2, b / 2, n, m, 4 * cur);
                ans += 4 * cur;
            }
        }
        printf("%lld\n", ans);
    }
    
    return 0;
}