分数模板

struct fraction {
	long long numerator; // 分子
	long long denominator; // 分母
	fraction() {
		numerator = 0;
		denominator = 1;
	}
	fraction(long long num) {
		numerator = num;
		denominator = 1;
	}
	fraction(long long a, long long b) {
		numerator = a;
		denominator = b;
		this->reduction();
	}
 
	void operator = (const long long num) {
		numerator = num;
		denominator = 1;
		this->reduction();
	}
 
	void operator = (const fraction &b) {
		numerator = b.numerator;
		denominator = b.denominator;
		this->reduction();
	}
 
	fraction operator + (const fraction &b) const {
		long long gcdnum = __gcd(denominator, b.denominator);
		fraction tmp = fraction(numerator*(b.denominator/gcdnum) + b.numerator*(denominator/gcdnum), denominator/gcdnum*b.denominator);
		tmp.reduction();
		return tmp;
	}
 
	fraction operator + (const int &b) const {
		return ((*this) + fraction(b));
	}
 
	fraction operator - (const fraction &b) const {
		return ((*this) + fraction(-b.numerator, b.denominator));
	}
 
	fraction operator - (const int &b) const {
		return ((*this) - fraction(b));
	}
 
	fraction operator * (const fraction &b) const {
		fraction tmp = fraction(numerator*b.numerator, denominator * b.denominator);
		tmp.reduction();
		return tmp;
	}
 
	fraction operator * (const int &b) const {
		return ((*this) * fraction(b));
	}
 
	fraction operator / (const fraction &b) const {
		return ((*this) * fraction(b.denominator, b.numerator));
	}
 
	void reduction() {
		if (numerator == 0) {
			denominator = 1;
			return;
		}
		long long gcdnum = __gcd(numerator, denominator);
		numerator /= gcdnum;
		denominator /= gcdnum;
	}
}