Problem: There is a polyline going through points (0, 0) – (x, x) – (2x, 0) – (3x, x) – (4x, 0) – ... - (2kx, 0) – (2kx + x, x) – .... 

We know that the polyline passes through the point (a, b). Find minimum positive value x such that it is true or determine that there is no such x.

Input

Only one line containing two positive integers a and b (1 ≤ a, b ≤ 109).

Output

Output the only line containing the answer. Your answer will be considered correct if its relative or absolute error doesn't exceed 10 - 9. If there is no such x then output  - 1 as the answer.

Examples

Input

3 1


Output

1.000000000000


Input

1 3


Output

-1


Input

4 1


Output

1.250000000000

Note

You can see following graphs for sample 1 and sample 3. 

<image> <image>

Solution (in JAVA):

Solution:
import java.io.InputStream;
import java.io.IOException;
import java.io.PrintWriter;
import java.util.ArrayDeque;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.BitSet;
import java.util.Comparator;
import java.util.Deque;
import java.util.HashMap;
import java.util.HashSet;
import java.util.InputMismatchException;
import java.util.Map;
import java.util.PriorityQueue;
import java.math.BigDecimal;
import java.math.BigInteger;
    
public class Main{

static final InputStream in=System.in;
static final PrintWriter out=new PrintWriter(System.out);
static final int INF=Integer.MAX_VALUE;
static final long LINF=Long.MAX_VALUE/2;

public static void main(String[] args) throws IOException{
InputReader ir=new InputReader(in);
int a=ir.nextInt();
int b=ir.nextInt();
if(a<b) out.println(-1);
else if(a==b) out.println(a);
else{
  double ans=Double.MAX_VALUE;
//   x=(a+b)/(n+1)>=b&&n%2==1
//==>xmax=(a+b)/i; (i=(int)(a+b)/b; i=(i%2==1)?i-1:i;
  int i=(a+b)/b; i=(i%2==1)?i-1:i;
  ans=Math.min(ans,(double)(a+b)/(double)i);
  i=(a-b)/b; i=(i%2==1)?i-1:i;
  ans=Math.min(ans,(double)(a-b)/(double)i);
  out.printf("%.15f\n",ans);
}
out.flush();
}

static class InputReader {
private InputStream in;
private byte[] buffer=new byte[1024];
private int curbuf;
private int lenbuf;

public InputReader(InputStream in) {this.in=in;}
  
public int readByte() {
if(lenbuf==-1) throw new InputMismatchException();
if(curbuf>=lenbuf){
curbuf= 0;
try{
lenbuf=in.read(buffer);
}
catch (IOException e) {
throw new InputMismatchException();
}
if(lenbuf<=0)
return -1;
}
return buffer[curbuf++];
}

public boolean isSpaceChar(int c){return !(c>=33&&c<=126);}

private int skip() {int b; while((b = readByte())!=-1&&isSpaceChar(b)); return b;}

public String next() {
int b=skip();
StringBuilder sb=new StringBuilder();
while(!isSpaceChar(b)){
sb.appendCodePoint(b);
b=readByte();
}
return sb.toString();
}
 
public int nextInt() {
int c=readByte();
while (isSpaceChar(c)) c=readByte();
boolean minus=false;
if (c=='-') {
minus=true;
c=readByte();
}
int res=0;
do{
if(c<'0'||c>'9') throw new InputMismatchException();
res=res*10+c-'0';
c=readByte();
}while(!isSpaceChar(c));
return (minus)?-res:res;
}

public long nextLong() {
int c=readByte();
while (isSpaceChar(c)) c=readByte();
boolean minus=false;
if (c=='-') {
minus=true;
c=readByte();
}
long res = 0;
do{
if(c<'0'||c>'9') throw new InputMismatchException();
res=res*10+c-'0';
c=readByte();
}while(!isSpaceChar(c));
return (minus)?-res:res;
}

public double nextDouble(){return Double.parseDouble(next());}

public BigInteger nextBigInteger(){return new BigInteger(next());}

public int[] nextIntArray(int n){
int[] a=new int[n];
for(int i=0;i<n;i++) a[i]=nextInt();
return a;
}
}
}