fraction class

struct NOS { 
	ll num,den;
	NOS() {}
	NOS(ll numn) : num(num) {den = 1;}
	NOS(ll num,ll den) : num(num),den(den) {
	    ll G = __gcd(num, den);
	    num /= G;
	    den /= G;
	}
	NOS(const NOS &p) : num(p.num),den(p.den) {}
	NOS operator + (const NOS &p) const { 
		ll num_=num*p.den+den*p.num,den_=den*p.den;
		ll G=__gcd(num_,den_);
		num_/=G; den_/=G;
		return NOS(num_,den_);
	}
	NOS operator - (const NOS &p) const {
		ll num_=num*p.den-den*p.num,den_=den*p.den;
		ll G=__gcd(num_,den_);
		num_/=G; den_/=G;
		return NOS(num_,den_);
	}
	NOS operator * (const NOS &p) const { 
	    ll a = num, b = den, c = p.num, d = p.den;
	    ll G1 = __gcd(a, d), G2 = __gcd(b, c);
	    a /= G1; d /= G1;
	    b /= G2; c /= G2;
	    a *= c;
	    b *= d;
	    ll G = __gcd(a, b); //extra
	    a /= G; b /= G;     //extra
	    return NOS(a, b);
	}
	bool operator != (const NOS &p) const {
		return (p.num != num or p.den != den);
	}
	bool operator == (const NOS &p) const {
		return (p.num == num and p.den == den);
	}
};