Frac

  1. 定义即为 frac a(nume,deno,sign)，含义分别为分子、分母、符号（\(-1\) 为负，\(1\) 为正）。
  2. Inv(a) 为求 \(a\) 的逆元。
  3. pout(a) 为带换行的输出分数 \(a\)，可以自行根据需求调整。
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namespace Frac
{
    inline int Gcd(int a,int b)
    {
        int az=__builtin_ctz(a),bz=__builtin_ctz(b);
        int z=min(az,bz),tmp; b>>=bz;
        while(a) a>>=az,tmp=a-b,az=__builtin_ctz(tmp),b=min(a,b),a=abs(tmp);
        return b<<z;
    }
    inline int Lcm(int a,int b)
    {
        return a*b/Gcd(a,b);
    }
    void Exgcd(int a,int b,int &x,int &y)
    {
        if(!b) return x=1,y=0,void();
        Exgcd(b,a%b,y,x),y-=x*(a/b);
    }
    void Abs(int &a)
    {
        return a=a<0?-a:a,void();
    }
    struct frac
    {
        int nume,deno,sign;
        frac(int Nume=0,int Deno=0,int Sign=0):nume(Nume),deno(Deno),sign(Sign) {}
        inline frac operator = (const frac &T) {this->nume=T.nume,this->deno=T.deno,this->sign=T.sign; return *this;}
        inline void Reduce()
        {
            int tmp=Gcd(nume,deno);
            nume/=tmp,deno/=tmp;
        }
        inline frac operator - ()
        {
            return frac(nume,deno,-sign);
        }
        inline friend frac operator + (frac a,frac b)
        {
            frac res;
            res.deno=Lcm(a.deno,b.deno);
            if(a.sign==b.sign) res.sign=a.sign,res.nume=res.deno/a.deno*a.nume+res.deno/b.deno*b.nume;
            else if(b.sign==-1) res.nume=res.deno/a.deno*a.nume-res.deno/b.deno*b.nume,res.nume<0?res.sign=-1:res.sign=1,Abs(res.nume);
            else if(a.sign==-1) res.nume=res.deno/b.deno*b.nume-res.deno/a.deno*a.nume,res.nume<0?res.sign=-1:res.sign=1,Abs(res.nume);
            res.Reduce();
            return res;
        }
        inline friend frac operator - (frac a,frac b) {return a+(-b);}
        inline friend frac operator * (frac a,frac b)
        {
            frac res;
            res.nume=a.nume*b.nume,res.deno=a.deno*b.deno,res.sign=a.sign*b.sign;
            res.Reduce();
            return res;
        }
        inline friend frac operator / (frac a,frac b) {return a*(frac(b.deno,b.nume,b.sign));}
        inline friend bool operator == (frac a,frac b) {return a.nume==b.nume&&a.deno==b.deno&&a.sign==b.sign;}
        inline friend bool operator > (frac a,frac b)
        {
            if(a.sign!=b.sign) return a.sign>b.sign;
            int tmp=Lcm(a.deno,b.deno);
            return tmp/a.deno*a.nume>tmp/b.deno*b.nume;
        }
        inline friend bool operator < (frac a,frac b)
        {
            if(a.sign!=b.sign) return a.sign<b.sign;
            int tmp=Lcm(a.deno,b.deno);
            return tmp/a.deno*a.nume<tmp/b.deno*b.nume;
        }
        inline friend bool operator >= (frac a,frac b) {return a>b||a==b;}
        inline friend bool operator <= (frac a,frac b) {return a<b||a==b;}
        inline frac operator += (const frac &T) {*this=*this+T; return *this;}
        inline frac operator -= (const frac &T) {*this=*this-T; return *this;}
        inline frac operator *= (const frac &T) {*this=*this*T; return *this;}
        inline frac operator /= (const frac &T) {*this=*this/T; return *this;}
    };
    inline int Inv(frac a)
    {
        a.nume%=a.deno;
        if(a.sign==-1) a.nume=a.deno-a.nume;
        int X=0,Y=0; Exgcd(a.nume,a.deno,X,Y);
        return (X%a.deno+a.deno)%a.deno;
    }
    inline void fout(frac a)
    {
        if(a.deno==1) write(a.sign*a.nume,'\n');
        else write(a.sign*a.nume,'/'),write(a.deno,'\n');
    }
}