// fraction.cs by M.Inamori 7/7/03
// modified 7/23/03

using System;

public class Fraction {
	private long	a;
	private long	b;
	public Fraction() { a = 0; b = 1; }
	public Fraction(long x) { a = x; b = 1; }
	public Fraction(long x, long y) { a = x; b = y; normalize(); }
	private static long add(long x, long y) {
		if((y > 0 && x > Int64.MaxValue - y) || (y < 0 && -x > Int64.MaxValue + y))
			throw(new System.OverflowException());
		return x + y;
	}
	private static long subtract(long x, long y) {
		if((y > 0 && -x > Int64.MaxValue - y) || (y < 0 && x > Int64.MaxValue + y))
			throw(new System.OverflowException());
		return x - y;
	}
	private static long multiple(long x, long y) {
		if(y == 0)
			return 0;
		
		long	z = System.Math.Abs(Int64.MaxValue / y);
		long	__x = System.Math.Abs(x);
		if(z < __x)
			throw(new System.OverflowException());
		return x * y;
	}
	public static Fraction operator +(Fraction f) {
		return f.Copy();
	}
	public static Fraction operator -(Fraction f) {
		Fraction	f1 = new Fraction();
		f1.a = -f.a; f1.b = f.b;
		return f1;
	}
	public static bool operator ==(Fraction f1, Fraction f2) {
		return f1.a == f2.a && f1.b == f2.b;
	}
	public static bool operator !=(Fraction f1, Fraction f2) {
		return f1.a != f2.a || f1.b != f2.b;
	}
	public static bool operator >(Fraction f1, Fraction f2) {
		return less(f2, f1);
	}
	public static bool operator <(Fraction f1, Fraction f2) {
		return less(f1, f2);
	}
	public static bool operator >=(Fraction f1, Fraction f2) {
		return !less(f1, f2);
	}
	public static bool operator <=(Fraction f1, Fraction f2) {
		return !less(f2, f1);
	}
	public static Fraction operator +(Fraction f1, Fraction f2) {
		return new Fraction(add(multiple(f1.a, f2.b), multiple(f1.b, f2.a)),
														multiple(f1.b, f2.b));
	}
	public static Fraction operator -(Fraction f1, Fraction f2) {
		return new Fraction(f1.a * f2.b - f1.b * f2.a, f1.b * f2.b);
	}
	public static Fraction operator *(Fraction f1, Fraction f2) {
		Fraction	result = new Fraction(f1.a, f2.b);
		long	r_a = result.a;
		long	r_b = result.b;
		result.a = f2.a; result.b = f1.b;
		result.normalize();
		result.a = multiple(result.a, r_a); result.b = multiple(result.b, r_b);
		return result;
	}
	public static Fraction operator /(Fraction f1, Fraction f2) {
		Fraction	result = new Fraction(f1.a, f2.a);
		long	r_a = result.a;
		long	r_b = result.b;
		result.a = f2.b; result.b = f1.b;
		result.normalize();
		result.a = multiple(result.a, r_a); result.b = multiple(result.b, r_b);
		return result;
	}
	private static bool less(Fraction f1, Fraction f2) {
		try {
			return multiple(f1.a, f2.b) < multiple(f2.a, f1.b);
		}
		catch(System.OverflowException e) {
			if(f1 == f2)
				return false;
			long	div1, div2;
			long	f1_a, f1_b, f2_a, f2_b;
			f1_a = f1.a; f1_b = f1.b; f2_a = f2.a; f2_b = f2.b;
			while(true) {
				div1 = f1_a / f1_b; div2 = f2_a / f2_b;
				if(div1 != div2)
					return div1 < div2;
				f1_a %= f1_b; f2_a %= f2_b;
				div1 = f1_b / f1_a; div2 = f2_b / f2_a;
				if(div1 != div2)
					return div1 > div2;
				f1_b %= f1_a; f2_b %= f2_a;
			}
		}
	}
	private void normalize() {
		long	a1, b1, a2, f;
		a1 = a; b1 = b;
		f = 1;
		while(true) {
			if((a2 = a1 % b1) == 0) {
				f = b1;
				break;
			}
			if((b1 = b1 % a1) == 0) {
				f = a1;
				break;
			}
			a1 = a2;
		}
		a /= f; b /= f;
		if(b < 0) {
			a = -a;
			b = -b;
		}
	}
	public override bool Equals(object o) {
		return a == ((Fraction)o).a && b == ((Fraction)o).b;
	}
	public override int GetHashCode() {
		return (int)((a + b) & 0x7FFFFFFF);
	}
	public Fraction Copy() {
		Fraction	f = new Fraction();
		f.a = a; f.b = b;
		return f;
	}
	public override string ToString() {
		if(b == 1)
			return a.ToString();
		else
			return a + "/" + b;
	}
}