Problem: In an electric circuit, when two resistors R_1 and R_2 are connected in parallel, the equivalent resistance R_3 can be derived from the following formula:

* \frac{1}{R_1} + \frac{1}{R_2} = \frac{1}{R_3}



Given R_1 and R_2, find R_3.

Constraints

* 1 \leq R_1, R_2 \leq 100
* R_1 and R_2 are integers.

Input

The input is given from Standard Input in the following format:


R_1 R_2


Output

Print the value of R_3.

The output is considered correct if the absolute or relative error is at most 10^{-6}.

Examples

Input

2 3


Output

1.2000000000


Input

100 99


Output

49.7487437186

Solution (in CPP):

Solution:
#pragma GCC optimize(2)
#include <cstdio>
using namespace std;

inline char nc()
{
    static char buf[100000],*p1=buf,*p2=buf;
    return p1==p2&&(p2=(p1=buf)+fread(buf,1,100000,stdin),p1==p2)?EOF:*p1++;
}

inline void read(double& sum)
{
    char ch; sum=0;
    ch=nc();
    while(!(ch>='0'&&ch<='9')) ch=nc();
    while(ch>='0'&&ch<='9') sum=sum*10+ch-48,ch=nc();
}

int main()
{
	double a,b;
	read(a),read(b);
	printf("%.6lf\n",(a*b)/(a+b));
	return 0;
}