To become the king of Codeforces, Kuroni has to solve the following problem.
He is given $n$ numbers $a_1, a_2, \dots, a_n$. Help Kuroni to calculate $\prod_{1\le i<j\le n} |a_i – a_j|$. As result can be very big, output it modulo $m$.
If you are not familiar with short notation, $\prod_{1\le i<j\le n} |a_i – a_j|$ is equal to $|a_1 – a_2|\cdot|a_1 – a_3|\cdot$ $\dots$ $\cdot|a_1 – a_n|\cdot|a_2 – a_3|\cdot|a_2 – a_4|\cdot$ $\dots$ $\cdot|a_2 – a_n| \cdot$ $\dots$ $\cdot |a_{n-1} – a_n|$. In other words, this is the product of $|a_i – a_j|$ for all $1\le i < j \le n$.Input
The first line contains two integers $n$, $m$ ($2\le n \le 2\cdot 10^5$, $1\le m \le 1000$) — number of numbers and modulo.
The second line contains $n$ integers $a_1, a_2, \dots, a_n$ ($0 \le a_i \le 10^9$).Output
Output the single number — $\prod_{1\le i<j\le n} |a_i – a_j| \bmod m$.Examplesinput
2 10 8 5
output
3
input
3 12 1 4 5
output
0
input
3 7 1 4 9
output
1
Note
In the first sample, $|8 – 5| = 3 \equiv 3 \bmod 10$.
In the second sample, $|1 – 4|\cdot|1 – 5|\cdot|4 – 5| = 3\cdot 4 \cdot 1 = 12 \equiv 0 \bmod 12$.
In the third sample, $|1 – 4|\cdot|1 – 9|\cdot|4 – 9| = 3 \cdot 8 \cdot 5 = 120 \equiv 1 \bmod 7$.
Solution:
#include <bits/stdc++.h> using namespace std; 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) { #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, int64_t>::value, Modular>::type& operator*=(const Modular& rhs) { int64_t q = static_cast<int64_t>(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())); } template <typename U> friend const Modular<U>& abs(const Modular<U>& v) { return v; } 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 U> friend std::istream& operator>>(std::istream& 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 T> std::ostream& operator<<(std::ostream& stream, const Modular<T>& number) { return stream << number(); } template <typename T> std::istream& operator>>(std::istream& stream, Modular<T>& number) { typename common_type<typename Modular<T>::Type, int64_t>::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::sync_with_stdio(false); cin.tie(0); int n; cin >> n >> md; vector<int> a(n); for (int i = 0; i < n; i++) { cin >> a[i]; } if (n > md) { cout << 0 << '\n'; } else { Mint ans = 1; for (int i = 0; i < n; i++) { for (int j = i + 1; j < n; j++) { ans *= abs(a[i] - a[j]); } } cout << ans << '\n'; } return 0; }