Problem: For some reason in many American cartoons anvils fall from time to time onto heroes' heads. Of course, safes, wardrobes, cruisers, planes fall sometimes too... But anvils do so most of all.

Anvils come in different sizes and shapes. Quite often they get the hero stuck deep in the ground. But have you ever thought who throws anvils from the sky? From what height? We are sure that such questions have never troubled you!

It turns out that throwing an anvil properly is not an easy task at all. Let's describe one of the most popular anvil throwing models.

Let the height p of the potential victim vary in the range [0;a] and the direction of the wind q vary in the range [ - b;b]. p and q could be any real (floating) numbers. Then we can assume that the anvil will fit the toon's head perfectly only if the following equation has at least one real root: 

<image>

Determine the probability with which an aim can be successfully hit by an anvil.

You can assume that the p and q coefficients are chosen equiprobably and independently in their ranges.

Input

The first line contains integer t (1 ≤ t ≤ 10000) — amount of testcases.

Each of the following t lines contain two space-separated integers a and b (0 ≤ a, b ≤ 106).

Pretests contain all the tests with 0 < a < 10, 0 ≤ b < 10.

Output

Print t lines — the probability of a successful anvil hit for each testcase. The absolute or relative error of the answer should not exceed 10 - 6.

Examples

Input

2
4 2
1 2


Output

0.6250000000
0.5312500000

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.*;
/*
 * 	Heart beats fast
 * 		Colors and promises
 * 			How to be brave
 * 				How can I love when I am afraid to fall...
 */
//read the question correctly (is y a vowel? what are the exact constraints?)
//look out for SPECIAL CASES (n=1?) and overflow (ll vs int?)
public class Main
{
	public static void main(String[] args)
	{
		int t=ni();
		while(t-->0)
		{
			int a=ni(),b=ni();
			if(b==0)
				pr(1);
			else if(a==0)
				pr(0.5);
			else if(a>=4*b)
				pr(1-((b+0.0)/a));
			else
				pr(0.5+(a/(16.0*b)));
		}
		
		System.out.print(output);
	}
	
	
	
	///////////////////////////////////////////
	///////////////////////////////////////////
	///template from here
	static interface combiner
	{
		public int combine(int a, int b);
	}
	static final int mod=1000000007;
	static final double eps=1e-8;
	static final long inf=100000000000000000L;
	static Reader in=new Reader();
	static StringBuilder output=new StringBuilder();
	static Random rn=new Random();
	public static void sort(int[]a)
	{
		int te;
		for(int i=0; i<a.length; i++)
		{
			te=rn.nextInt(a.length);
			if(i!=te)
			{
				a[i]^=a[te];
				a[te]^=a[i];
				a[i]^=a[te];
			}
		}
		Arrays.sort(a);
	}
	public static void sort(long[]a)
	{
		int te;
		for(int i=0; i<a.length; i++)
		{
			te=rn.nextInt(a.length);
			if(i!=te)
			{
			a[i]^=a[te];
			a[te]^=a[i];
			a[i]^=a[te];
			}
		}
		Arrays.sort(a);
	}public static void sort(double[]a)
	{
		int te;
		double te1;
		for(int i=0; i<a.length; i++)
		{
			te=rn.nextInt(a.length);
			if(i!=te)
			{
			te1=a[te];
			a[te]=a[i];
			a[i]=te1;
			}
		}
		Arrays.sort(a);
	}
	public static void sort(int[][]a)
	{
		Arrays.sort(a, new Comparator<int[]>()
		{
			public int compare(int[]a,int[]b)
			{
				if(a[0]>b[0])
					return 1;
				if(b[0]>a[0])
					return -1;
				return 0;
			}
		});
	}
	static int lowerbound(int[]a, int key)
	{
		/*
		 * returns index of smallest element larger than equal to given element between indices l and r inclusive
		 */
		int low=0,high=a.length-1,mid=(low+high)/2;
		while(low<high)
		{
			if(a[mid] >= key)
				high=mid;
			else
				low=mid+1;
			mid=(low+high)/2;
		}
		return mid;
	}
	static int upperbound(int[]a, int key)
	{
		/*
		 * returns index of largest element smaller than equal to given element
		 */
		int low=0,high=a.length-1,mid=(low+high+1)/2;
		while(low<high)
		{
			if(a[mid] <= key)
				low=mid;
			else
				high=mid-1;
			mid=(low+high+1)/2;
		}
		return mid;
	}
	static int lowerbound(int[]a, int l, int r, int key)
	{
		/*
		 * returns index of smallest element larger than equal to given element between indices l and r inclusive
		 */
		int low=l,high=r,mid=(low+high)/2;
		while(low<high)
		{
			if(a[mid] >= key)
				high=mid;
			else
				low=mid+1;
			mid=(low+high)/2;
		}
		return mid;
	}
	static int upperbound(int[]a, int l, int r, int key)
	{
		/*
		 * returns index of largest element smaller than equal to given element
		 */
		int low=l,high=r,mid=(low+high+1)/2;
		while(low<high)
		{
			if(a[mid] <= key)
				low=mid;
			else
				high=mid-1;
			mid=(low+high+1)/2;
		}
		return mid;
	}
	static class pair
	{
		int a,b;
		pair()
		{
			
		}
		pair(int c,int d)
		{
			a=c;
			b=d;
		}	
	}
	void sort(pair[]a)
	{
		Arrays.sort(a,new Comparator<pair>()
				{
			@Override
			public int compare(pair a,pair b)
			{
				if(a.a>b.a)
					return 1;
				if(b.a>a.a)
				return -1;
				return 0;
			}
				});
	}
	static int log2n(long a)
	{
		int te=0;
		while(a>0)
		{
			a>>=1;
			++te;
		}
		return te;
	}
	static class iter
	{
		vecti a;
		int zin=0;
		iter(vecti b)
		{
			a=b;
		}
		public boolean hasNext()
		{
			if(a.size>zin)
				return true;
			return false;
		}
		public int next()
		{
			return a.a[zin++];
		}
		public void previous()
		{
			zin--;
		}
	}
	static class vecti
	{
		int a[],size;
		vecti()
		{
			a=new int[10];
			size=0;
		}
		vecti(int n)
		{
			a=new int[n];
			size=0;
		}
		public void add(int b)
		{
			if(++size==a.length)
				a=Arrays.copyOf(a, 2*size);
			a[size-1]=b;
		}
		public void sort()
		{
			Arrays.sort(a, 0, size);
		}
		public void sort(int l, int r)
		{
			Arrays.sort(a, l, r);
		}
		public iter iterator()
		{
			return new iter(this);
		}
	}
	static class lter
	{
		vectl a;
		int curi=0;
		lter(vectl b)
		{
			a=b;
		}
		public boolean hasNext()
		{
			if(a.size>curi)
				return true;
			return false;
		}
		public long next()
		{
			return a.a[curi++];
		}
		public long prev()
		{
			return a.a[--curi];
		}
	}
	static class vectl
	{
		long a[];
		int size;
		vectl()
		{
			a=new long[10];
			size=0;
		}
		vectl(int n)
		{
			a=new long[n];
			size=0;
		}
		public void add(long b)
		{
			if(++size==a.length)
				a=Arrays.copyOf(a, 2*size);
			a[size-1]=b;
		}
		public void sort()
		{
			Arrays.sort(a, 0, size);
		}
		public void sort(int l, int r)
		{
			Arrays.sort(a, l, r);
		}
		public lter iterator()
		{
			return new lter(this);
		}
	}
	static class dter
	{
		vectd a;
		int curi=0;
		dter(vectd b)
		{
			a=b;
		}
		public boolean hasNext()
		{
			if(a.size>curi)
				return true;
			return false;
		}
		public double next()
		{
			return a.a[curi++];
		}
		public double prev()
		{
			return a.a[--curi];
		}
	}
	static class vectd
	{
		double a[];
		int size;
		vectd()
		{
			a=new double[10];
			size=0;
		}
		vectd(int n)
		{
			a=new double[n];
			size=0;
		}
		public void add(double b)
		{
			if(++size==a.length)
				a=Arrays.copyOf(a, 2*size);
			a[size-1]=b;
		}
		public void sort()
		{
			Arrays.sort(a, 0, size);
		}
		public void sort(int l, int r)
		{
			Arrays.sort(a, l, r);
		}
		public dter iterator()
		{
			return new dter(this);
		}
	}
	//output functions////////////////
	static void pr(Object a){output.append(a+"\n");}
	static void pr(){output.append("\n");}
	static void p(Object a){output.append(a);}
	static void pra(int[]a){for(int i:a)output.append(i+" ");output.append("\n");}
	static void pra(long[]a){for(long i:a)output.append(i+" ");output.append("\n");}
	static void pra(String[]a){for(String i:a)output.append(i+" ");output.append("\n");}
	static void pra(double[]a){for(double i:a)output.append(i+" ");output.append("\n");}
	static void sop(Object a){System.out.println(a);}
	static void flush(){System.out.println(output);output=new StringBuilder();}
	//////////////////////////////////
	//input functions/////////////////
	static int ni(){return in.nextInt();}
	static long nl(){return Long.parseLong(in.next());}
	static String ns(){return in.next();}
	static double nd(){return Double.parseDouble(in.next());}
	static int[] nia(int n){int a[]=new int[n];for(int i=0; i<n; i++)a[i]=ni();return a;}
	static int[] pnia(int n){int a[]=new int[n+1];for(int i=1; i<=n; i++)a[i]=ni();return a;}
	static long[] nla(int n){long a[]=new long[n];for(int i=0; i<n; i++)a[i]=nl();return a;}
	static String[] nsa(int n){String a[]=new String[n];for(int i=0; i<n; i++)a[i]=ns();return a;}
	static double[] nda(int n){double a[]=new double[n];for(int i=0; i<n; i++)a[i]=nd();return a;}
	static vecti niv(int n) {vecti a=new vecti(n);a.size=n;for(int i=0; i<n; i++)a.a[i]=ni();return a;}
	static vectl nlv(int n) {vectl a=new vectl(n);a.size=n;for(int i=0; i<n; i++)a.a[i]=nl();return a;}
	static vectd ndv(int n) {vectd a=new vectd(n);a.size=n;for(int i=0; i<n; i++)a.a[i]=nd();return a;}
	//////////////////////////////////
	//some utility functions
	static void exit(){System.exit(0);}
	static void psort(int[][] a)
	{
		Arrays.sort(a, new Comparator<int[]>()
		{
			@Override
			public int compare(int[]a,int[]b)
			{
				if(a[0]>b[0])
					return 1;
				else if(b[0]>a[0])
					return -1;
				return 0;
			}
		});
	}
	static String pr(String a, long b)
	{
		String c="";
		while(b>0)
		{
			if(b%2==1)
				c=c.concat(a);
			a=a.concat(a);
			b>>=1;
		}
		return c;
	}
	static long powm(long a, long b, long m)
	{
		long an=1;
		long c=a;
		while(b>0)
		{
			if(b%2==1)
				an=(an*c)%m;
			c=(c*c)%m;
			b>>=1;
		}
		return an;
	}
	static int gcd(int a, int b)
	{
		if(b==0)
			return a;
		else
			return gcd(b, a%b);
	}
	static class Reader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;
        public Reader() {
            reader = new BufferedReader(new InputStreamReader(System.in), 32768);
            tokenizer = null;
        }
        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }
        public int nextInt() {
            return Integer.parseInt(next());
        }
        public long nextLong() {
        	return Long.parseLong(next());
        }
        public double nextDouble() {
        	return Double.parseDouble(next());
        }
    }
}