Submission #967614

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Source Code Expand

#include <bits/stdc++.h>

using namespace std;
#define FOR(i,n) for(int i = 0; i < (n); i++)
#define sz(c) ((int)c.size())
#define ten(n) ((int)1e##n)
using ll = long long;

template<typename ...> static inline int getchar_unlocked(void) { return getchar(); }
template<typename ...> static inline void putchar_unlocked(int c) { putchar(c); }
#define mygc(c) (c)=getchar_unlocked()
#define mypc(c) putchar_unlocked(c)
void reader(int& x) { int k, m = 0; x = 0; for (;;) { mygc(k); if (k == '-') { m = 1; break; }if ('0' <= k&&k <= '9') { x = k - '0'; break; } }for (;;) { mygc(k); if (k<'0' || k>'9')break; x = x * 10 + k - '0'; }if (m) x = -x; }
void reader(ll& x) { int k, m = 0; x = 0; for (;;) { mygc(k); if (k == '-') { m = 1; break; }if ('0' <= k&&k <= '9') { x = k - '0'; break; } }for (;;) { mygc(k); if (k<'0' || k>'9')break; x = x * 10 + k - '0'; }if (m) x = -x; }
int reader(char c[]) { int i, s = 0; for (;;) { mygc(i); if (i != ' '&&i != '\n'&&i != '\r'&&i != '\t'&&i != EOF) break; }c[s++] = i; for (;;) { mygc(i); if (i == ' ' || i == '\n' || i == '\r' || i == '\t' || i == EOF) break; c[s++] = i; }c[s] = '\0'; return s; }
int reader(string& c) { int i; for (;;) { mygc(i); if (i != ' '&&i != '\n'&&i != '\r'&&i != '\t'&&i != EOF) break; }c.push_back(i); for (;;) { mygc(i); if (i == ' ' || i == '\n' || i == '\r' || i == '\t' || i == EOF) break; c.push_back(i); }; return sz(c); }
template <class T, class S> void reader(T& x, S& y) { reader(x); reader(y); }
template <class T, class S, class U> void reader(T& x, S& y, U& z) { reader(x); reader(y); reader(z); }
template <class T, class S, class U, class V> void reader(T& x, S& y, U& z, V & w) { reader(x); reader(y); reader(z); reader(w); }
void writer(int x, char c) { int s = 0, m = 0; char f[10]; if (x<0)m = 1, x = -x; while (x)f[s++] = x % 10, x /= 10; if (!s)f[s++] = 0; if (m)mypc('-'); while (s--)mypc(f[s] + '0'); mypc(c); }
void writer(ll x, char c) { int s = 0, m = 0; char f[20]; if (x<0)m = 1, x = -x; while (x)f[s++] = x % 10, x /= 10; if (!s)f[s++] = 0; if (m)mypc('-'); while (s--)mypc(f[s] + '0'); mypc(c); }
void writer(const char c[]) { int i; for (i = 0; c[i] != '\0'; i++)mypc(c[i]); }
void writer(const char x[], char c) { int i; for (i = 0; x[i] != '\0'; i++)mypc(x[i]); mypc(c); }
template<class T> void writerLn(T x) { writer(x, '\n'); }
template<class T, class S> void writerLn(T x, S y) { writer(x, ' '); writer(y, '\n'); }
template<class T, class S, class U> void writerLn(T x, S y, U z) { writer(x, ' '); writer(y, ' '); writer(z, '\n'); }
template<class T> void writerArr(T x[], int n) { if (!n) { mypc('\n'); return; }FOR(i, n - 1)writer(x[i], ' '); writer(x[n - 1], '\n'); }
template<class T> void writerArr(vector<T>& x) { writerArr(x.data(), (int)x.size()); }

template<class T> T gcd(T a, T b) { return b ? gcd(b, a % b) : a; }
template<class T> T lcm(T a, T b) { return a / gcd(a, b) * b; }
ll mod_pow(ll a, ll n, ll mod) {
	ll ret = 1;
	ll p = a % mod;
	while (n) {
		if (n & 1) ret = ret * p % mod;
		p = p * p % mod;
		n >>= 1;
	}
	return ret;
}
template<class T> T extgcd(T a, T b, T& x, T& y) { for (T u = y = 1, v = x = 0; a;) { T q = b / a; swap(x -= q * u, u); swap(y -= q * v, v); swap(b -= q * a, a); } return b; }
template<class T> T mod_inv(T a, T m) { T x, y; extgcd(a, m, x, y); return (m + x % m) % m; }

using Pii = pair<int, int>;
using Pll = pair<ll, ll>;

class Primes {

	//素数列挙
	void init_prime() {
		fill(prime.begin(), prime.end(), 1);
		prime[0] = prime[1] = false;
		for (int i = 2; i * i < size; i++) if (prime[i]) {
			for (int j = i * 2; j <= size; j += i) prime[j] = false;
		}
		for (int i = 2; i <= size; i++) if (prime[i]) v_prime.push_back(i);
	}

public:

	vector<char> prime; //boolでも可能
	vector<int> v_prime;
	int size;

	Primes(int size = 1000000) : size(size), prime(size + 1) {
		init_prime();
		srand((unsigned int)time(NULL));
	}

	//因数分解
	vector<pair<int, int>> factorization(int x) {
		assert(x > 0);
		vector<pair<int, int>> ret;
		if (x == 1) return ret;

		for (int i = 0; i < (int)v_prime.size(); i++) {
			int y = v_prime[i];
			if (x % y == 0) {
				int cnt = 0;
				while (x % y == 0) { x /= y; cnt++; }
				ret.emplace_back(y, cnt);
				if (x == 1) break;
				if (x <= size && prime[x]) {
					ret.emplace_back(x, 1);
					x = 1;
					break;
				}
			}
		}

		if (x > size) ret.emplace_back(x, 1);
		return ret;
	}

	//約数関数 σ(n) 例えば σ(15) = 1 + 3 + 5 + 15
	int DivisorFunction(int n) {
		auto mp = factorization(n);
		ll ans = 1;
		for (auto kv : mp) {
			ans *= (pow((ll)kv.first, (ll)kv.second + 1) - 1) / (kv.first - 1);
		}
		return (int)ans;
	}

	vector<int> Divisors(int n) {
		auto mp = factorization(n);
		vector<int> ret(1, 1);
		for (auto it : mp) {
			int cur_size = (int)ret.size();
			auto inserter = back_inserter(ret);
			for (int j = 0; j < cur_size; j++) {
				int x = ret[j] * it.first;
				for (int i = 1; i <= it.second; i++, x *= it.first) {
					inserter++ = x;
				}
			}
		}
		return ret;
	}

	// 真の約数の和 = 約数関数σ(n) - n つまり、自身を含まない。
	// 真の約数の和 = n ならば 完全数
	// 真の約数の和 < n ならば 不足数
	// 真の約数の和 < n ならば 過剰数

	bool IsPerfectNumber(int n) { return DivisorFunction(n) - n == n; }
	//過剰数かどうか
	bool IsAbundantNumber(int n) { return DivisorFunction(n) - n > n; }
	//不足数かどうか
	bool IsDeficientNumber(int n) { return DivisorFunction(n) - n < n; }

	//radical 異なる素因数の積 504 = 2^3*3^2*7 より rad(504) = 2*3*7=42
	ll rad(int n) {
		int ret = 1;
		for (vector<int>::iterator it = v_prime.begin(); it != v_prime.end(); ++it) {
			int& y = *it;
			if (y * y > n) break;
			if (n % y == 0) {
				ret *= y;
				while (n % y == 0) { n /= y; }
				if (n <= size && prime[n])
					break;
			}
		}
		if (n != 1)
			ret *= n;
		return ret;
	}

	template<class T> bool is_prime(T n) {
		if (n <= size) return prime[(int)n] != 0;
		for (vector<int>::iterator it = v_prime.begin(); it != v_prime.end(); ++it) {
			int a = *it;
			if (((T)a)*a > n) return true;
			if (n%a == 0) return false;
		}
		assert(false);
		return true;
	}
};

Primes prs;

int main() {
	int n, k; reader(n, k);
	vector<int> a(n);
	FOR(i, n) {
		int x; reader(x);
		a[i] = gcd(x, k);
	}

	unordered_map<ll, ll> tbl;
	for (auto x : a) {
		tbl[x]++;
	}

	unordered_map<ll,ll> cnt;
	for(auto& kv : tbl) {
		int i = (int)kv.first;
		const int inv = k / i;

		auto dv = prs.Divisors(i);
		for(auto y : dv) {
			cnt[inv * y] += tbl[i];
		}
	}

	ll ans = 0;
	for (int i = 1; i <= k; i++) {
		ans += tbl[i] * cnt[i];
	}
	for (ll x : a) {
		if (x * x % k == 0) ans--;
	}
	ans /= 2;
	writerLn(ans);

	return 0;
}

Submission Info

Judge Result