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.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.math.BigInteger;
import java.util.ArrayList;
import java.util.Random;
import java.util.StringTokenizer;


public class Main {

	static boolean visited[] ; 
	static boolean ends[] ;
	static int lens[] ; 
	static int seeds[] ; 
	static int a[] ;
	static double total ; 
	public static ArrayList adj[] ; 
	public static void main(String[] args) throws IOException, InterruptedException {
		Scanner sc =  new Scanner(System.in) ;
		int t = sc.nextInt() ; 
		while(t-->0)
		{
			long a = sc.nextInt() ; 
			long b = sc.nextInt() ; 
			if(a==0 && b==0)
			{System.out.println(1);}
			else if(a==0)
			{System.out.println(0.5);;}
			else if(b==0)
			{System.out.println(1);}
			else if(b==a/4.0)
			{System.out.println(0.75);}
			else if(b>a/4.0)
			{System.out.println((a*a/8.0)/(2.0*b*a) + 0.5);;}
			else if(b<a/4.0)
			{System.out.println(1-((b*b*2.0)/(2.0*b*a)));;}
		}

	}



	public static long getN(long x)
	{
		long n = (long) Math.sqrt(x*2) ; 
		long y = n*(n+1)/2; 
		if(y==x)
			return n ; 
		else if(y>x)
			return n ; 
		else
			for (long i = n; ; i++)
			{
				y = i*(i+1)/2 ; 
				if(y>=x)
					return i ; 


			}	}








	public static void dfss(int root , int len)
	{
		visited[root]=true ; 
		if(ends[root] && root!=0) lens[root] = len ; 

		for (int i = 0; i < adj[root].size(); i++)
		{
			int c= (int) adj[root].get(i) ; 
			if(visited[c]==false)
				dfss(c, len+1);
		}
	}

	public static void pr(int root ,  int seed){
		visited[root] = true ;
		int dv = adj[root].size()-1 ; 
		if(root==0) dv++ ;

		for (int i = 0; i < adj[root].size(); i++)
		{
			int c = (int)adj[root].get(i) ; 
			seeds[c]=dv*seed ;
		}

		for (int i = 0; i < adj[root].size() ; i++)
		{
			int c = (int)adj[root].get(i) ; 
			if(visited[c]==false)
				pr(c , seeds[c]);

		}

	}


	public static String concatinate(String s ,int n)
	{
		if(s.length()==n)
			return s ; 
		else return concatinate("0"+s, n) ;
	}
	static class Scanner {
		StringTokenizer st;
		BufferedReader br;

		public Scanner(InputStream s) {
			br = new BufferedReader(new InputStreamReader(s));
		}

		public String next() throws IOException {
			while (st == null || !st.hasMoreTokens())
				st = new StringTokenizer(br.readLine());
			return st.nextToken();
		}

		public int nextInt() throws IOException {
			return Integer.parseInt(next());
		}

		public long nextLong() throws IOException {
			return Long.parseLong(next());
		}

		public String nextLine() throws IOException {
			return br.readLine();
		}

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

		public boolean ready() throws IOException {
			return br.ready();
		}
	}


	public static long getGCD(long n1, long n2) {
		if (n2 == 0) {
			return n1;
		}
		return getGCD(n2, n1 % n2);
	}

	public static int cnt1(int mat[][])  //how many swaps to be a 1 matrix
	{
		int m = mat.length ; 
		int c=0 ; 
		for (int i = 0; i < mat.length; i++)
		{
			for (int j = 0; j < mat.length; j++)
			{
				int x =  (i*m) +j ;
				if(x%2==0 && mat[i][j]==0)
					c++; 
				if(x%2!=0 && mat[i][j]==1)
					c++; 

			}
		}
		return c;
	}
	public static int cnt0(int mat[][])
	{
		int m = mat.length ; 
		int c=0 ; 
		for (int i = 0; i < mat.length; i++)
		{
			for (int j = 0; j < mat.length; j++)
			{
				int x =  (i*m) +j ; 
				if(x%2!=0 && mat[i][j]==0)
					c++; 
				if(x%2==0 && mat[i][j]==1)
					c++; 

			}
		}
		return c;
	}

	public static boolean canFit2(int x1, int y1 , int x2 , int y2 , int x3 , int y3){
		if(x1==x2)
			if(x1==x3)
				return true ; 
			else
				return false ;
		else
			if(x1==x3)
				return false ; 
			else
			{
				long a = 1l*(y2-y1)*(x3-x2) ; 
				long b = 1l*(y3-y2)*(x2-x1) ; 

				if(a==b)
					return true;
				else 
					return false ;

			}

	}
	public static void shuffle(long[] a2){
		if(a2.length==1)
			return ; 
		for (int i = 0; i < a2.length; i++)
		{
			Random rand = new Random();

			int  n = rand.nextInt(a2.length-1) + 0;

			long temp = a2[i] ; 
			a2[i] = a2[n] ; 
			a2[n] = temp ;
		}
	}
	public static int binary(long[]arr, int l, int r, long x)   /// begin by 0 and n-1
	{
		if (r>=l)
		{
			int mid = l + (r - l)/2;
			if (arr[mid]== x)
				return mid;
			if (arr[mid]> x)
				return binary(arr, l, mid-1, x);
			return binary(arr, mid+1, r, x);
		}
		return -1;
	}

	/// searching for the index of first elment greater than x
	public static int binary1(long[]arr , long x) {
		int low = 0, high = arr.length; // numElems is the size of the array i.e arr.size() 
		while (low != high) {
			int mid = (low + high) / 2; // Or a fancy way to avoid int overflow
			if (arr[mid] <= x) {
				/* This index, and everything below it, must not be the first element
				 * greater than what we're looking for because this element is no greater
				 * than the element.
				 */
				low = mid + 1;
			}
			else {
				/* This element is at least as large as the element, so anything after it can't
				 * be the first element that's at least as large.
				 */
				high = mid;
			}
		}
		return low ; // return high ; 
	}


	private static boolean triangle(int a, int b , int c){
		if(a+b>c && a+c>b && b+c>a)
			return true ; 
		else 
			return false ;
	}
	private static boolean segment(int a, int b , int c){
		if(a+b==c || a+c==b && b+c==a)
			return true ; 
		else 
			return false ;
	}
	private static int gcdThing(long a, long b) {
		BigInteger b1 = BigInteger.valueOf(a);
		BigInteger b2 = BigInteger.valueOf(b);
		BigInteger gcd = b1.gcd(b2);
		return gcd.intValue();
	}

	public static boolean is(int i){
		if(Math.log(i)/ Math.log(2) ==(int) (Math.log(i)/ Math.log(2)))
			return true ; 
		if(Math.log(i)/ Math.log(3) ==(int) (Math.log(i)/ Math.log(3)) )
			return true ; 
		if(Math.log(i)/ Math.log(6) ==(int) (Math.log(i)/ Math.log(6)) )
			return true ; 

		return false;

	}
	public static boolean contains(int b[] , int x)
	{
		for (int i = 0; i < b.length; i++)
		{
			if(b[i]==x)
				return true ;
		}
		return false ;
	}
	public static int binary(long []arr , long target , int low , long shift) {
		int high = arr.length; 
		while (low != high) {
			int mid = (low + high) / 2; 
			if (arr[mid]-shift <= target) {
				low = mid + 1;
			}
			else {
				high = mid;
			}
		}
		return low ; // return high ; 
	}
	public static boolean isLetter(char x){
		if(x+0 <=122 && x+0 >=97 )
			return true ;
		else if (x+0 <=90 && x+0 >=65 )
			return true ; 
		else return false; 
	}
	public static long getPrimes(long x ){
		if(x==2 || x==3 || x==1)
			return 2 ;
		if(isPrime(x))
			return 5 ;
		for (int i = 2; i*i<=x; i++)
		{
			if(x%i==0 && isPrime(i))
				return getPrimes(x/i) ;
		}
		return -1;
	}
	public static String solve(String x){

		int n = x.length() ; 
		String y = "" ;
		for (int i = 0; i < n-2; i+=2)
		{
			if(ifPalindrome(x.substring(i, i+2)))
				y+= x.substring(i, i+2) ;
			else 
				break ;
		}
		return y+ solve1(x.substring(y.length(),x.length())) ;

	}
	public static String solve1(String x){
		String y = x.substring(0 , x.length()/2) ; 
		return "" ;

	}
	public static String reverse(String x){
		String y ="" ;
		for (int i = 0; i < x.length(); i++)
		{
			y  = x.charAt(i) + y ;
		}
		return y ;
	}

	public static boolean ifPalindrome(String x){
		int numbers[] = new int[10] ; 
		for (int i = 0; i < x.length(); i++)
		{
			int z = Integer.parseInt(x.charAt(i)+"") ; 
			numbers[z] ++ ;
		}
		for (int i = 0; i < numbers.length; i++)
		{
			if(numbers[i]%2!=0)
				return false; 
		}
		return true ;	
	}

	public static int get(int n){
		return n*(n+1)/2 ; 
	}
	//		public static long getSmallestDivisor( long y){
	//			if(isPrime(y))
	//				return -1;
	//
	//			for (long i = 2; i*i <= y; i++)
	//			{
	//				if(y%i ==0)
	//				{
	//					return i;
	//				}
	//			}
	//			return -1;
	//		}
	//		public static void lis( []a , int n){
	//			int lis[] = new int[n] ; 
	//			Arrays.fill(lis,1) ; 
	//
	//			for(int i=1;i<n;i++)
	//				for(int j=0 ; j<i; j++)
	//					if (a[i].y>a[j].y &&  lis[i] < lis[j]+1)   
	//						lis[i] = lis[j] + 1;           
	//
	//			int max = lis[0];
	//
	//			for(int i=1; i<n ; i++)
	//				if (max < lis[i])
	//					max = lis[i] ;
	//			System.out.println(max);
	//
	//			ArrayList<Integer> s = new ArrayList<Integer>() ;
	//			for (int i = n-1; i >=0; i--)
	//			{
	//				if(lis[i]==max)
	//				{
	//					s.add(a[i].z);
	//					max --; 
	//				}
	//			}
	//
	//			for (int i = s.size()-1 ; i>=0 ;  i--)
	//			{
	//				System.out.print(s.get(i)+" ");
	//			}
	//
	//			return  ; 
	//		}
	public static int calcDepth(Vertix node){
		if(node.depth>0) return node.depth; 
		// meaning it has been updated before;
		if(node.parent != null)
			return 1+ calcDepth(node.parent);
		else
			return -1;
	}

	public static boolean isPrime (long num){
		if (num < 2) return false;
		if (num == 2) return true;
		if (num % 2 == 0) return false;
		for (int i = 3; i * i <= num; i += 2)
			if (num % i == 0) return false;
		return true;
	}


	public static ArrayList<Long> getDiv(Long n)
	{
		ArrayList<Long>  f = new ArrayList<Long>() ; 

		while (n%2==0)
		{
			if(!f.contains(2))f.add((long) 2) ;
			n /= 2;
		}

		// n must be odd at this point.  So we can
		// skip one element (Note i = i +2)
		for (long i = 3; i <= Math.sqrt(n); i+= 2)
		{
			// While i divides n, print i and divide n
			while (n%i == 0)
			{
				if(!f.contains(i))f.add(i);
				n /= i;
			}
		}

		// This condition is to handle the case whien
		// n is a prime number greater than 2
		if (n > 2)
			if(!f.contains(n))f.add(n);


		return f ;



	}

	//		public static boolean dfs(Vertix v , int target){
	//			try{
	//				visited[v.i]= true ;
	//			} catch (NullPointerException e)
	//			{
	//				System.out.println(v.i);
	//			}
	//			if(v.i == target)
	//
	//				return true ;
	//			for (int i =0 ; i< v.neighbours.size() ; i++)
	//			{ 
	//
	//				Vertix child = v.neighbours.get(i) ;
	//				if(child.i == target){
	//					found = true  ; 
	//				}
	//				if(visited[child.i]==false){
	//					found |= dfs(child, target) ;
	//				}
	//			}
	//			return found; 
	//		}









	public static class Vertix{
		long i ; 
		int depth ;
		ArrayList<Vertix> neighbours ; 
		Vertix parent ; 
		Vertix child ; 


		public Vertix(long i){
			this.i = i ;
			this.neighbours = new ArrayList<Vertix> () ;
			this.parent = null ;
			depth =-1;
			this.child = null ;
		}
	}

	public static class pair{
		int p ; 
		int x ;
		int y ;





		public pair(int p,int x, int y ){
			this.p=p;
			this.x=x ; 
			this.y=y ;


		}
		public boolean equals(pair s)
		{
			if(this.p==s.p && this.x==s.x && this.y==s.y)
				return true;
			else 
				return false;

		}





	}

	public static class pair2 implements Comparable<pair2>{
		int i ; 
		int j ;
		int index ; 

		public pair2(int i , int j , int index){
			this.i =i ;
			this.j = j ; 
			this.index = index ;
		}

		@Override
		public int compareTo(pair2 p) {
			if(this.j > p.j)
				return 1 ; 
			else if (this.j == p.j) return 0 ;
			else 
				return -1 ;
		}


	}


}