YouKn0wWho has two even integers x and y. Help him to find an integer n such that 1 ≤ n ≤ 2 ⋅ 10^{18} and n mod x = y mod n. Here, a mod b denotes the remainder of a after division by b. If there are multiple such integers, output any. It can be shown that such an integer always exists under the given constraints.

Input

The first line contains a single integer t (1 ≤ t ≤ 10^5) — the number of test cases.

The first and only line of each test case contains two integers x and y (2 ≤ x, y ≤ 10^9, both are even).

Output

For each test case, print a single integer n (1 ≤ n ≤ 2 ⋅ 10^{18}) that satisfies the condition mentioned in the statement. If there are multiple such integers, output any. It can be shown that such an integer always exists under the given constraints.

Example

Input


4
4 8
4 2
420 420
69420 42068


Output


4
10
420
9969128

Note

In the first test case, 4 mod 4 = 8 mod 4 = 0.

In the second test case, 10 mod 4 = 2 mod 10 = 2.

In the third test case, 420 mod 420 = 420 mod 420 = 0.
1
1000000000 1000000000

1000000000 

import java.util.*;
import java.io.*;
// import java.lang.*;
// import java.math.*;

public class Codeforces {
    static FastReader sc=new FastReader();
	static PrintWriter out=new PrintWriter(System.out);
	static long mod=1000000007;
	// static long mod=998244353;
	static int MAX=Integer.MAX_VALUE;
	static int MIN=Integer.MIN_VALUE;
	static long MAXL=Long.MAX_VALUE;
	static long MINL=Long.MIN_VALUE;
	static ArrayList<Integer> graph[];
	static long fact[];
	static StringBuffer sb;
	public static void main (String[] args) throws java.lang.Exception
	{
		// code goes here
		int t=I();
		outer:while(t-->0)
		{
			long a=L(),b=L();
			if(a==b){
				out.println(a);
			}else if(a>b){
				out.println(a+b);
			}else{
					long p=b%a;
					p/=2;
					out.println(b-p);
			}
		}
		out.close();
	}
	public static class pair
    {
    	long a;
    	long b;
    	public pair(long val,long index)
    	{
    	    a=val;
    	    b=index;
    	}
    }
	public static class myComp implements Comparator<pair>
	{
		//sort in ascending order.
		// public int compare(pair p1,pair p2)
		// {
		// 	if(p1.a==p2.a)
    	//     return 0;
    	//     else if(p1.a<p2.a)
    	//     return -1;
    	//     else
    	//     return 1;
		// }
		//sort in descending order.
		public int compare(pair p1,pair p2)
    	{
    	    if(p1.a==p2.a)
    	    return 0;
    	    else if(p1.a<p2.a)
    	    return 1;
    	    else
    	    return -1;
    	}
	}
	public static long nPr(int n,int r)
	{
		long ans=divide(fact(n),fact(n-r),mod);
		return ans;
	}
	public static long nCr(int n,int r)
	{
		long ans=divide(fact[n],mul(fact[n-r],fact[r]),mod);
		return ans;
	}
	public static long kadane(long a[],int n)  //largest sum subarray
	{
		long max_sum=Long.MIN_VALUE,max_end=0;
		for(int i=0;i<n;i++){
			max_end+=a[i];
			if(max_sum<max_end){max_sum=max_end;}
			if(max_end<0){max_end=0;}
		}
		return max_sum;
	}
	public static void DFS(int s,boolean visited[])
	{
		visited[s]=true;
		for(int i:graph[s]){
			if(!visited[i]){
				DFS(i,visited);
			}
		}
	}
	public static void setGraph(int n,int m)
	{
		graph=new ArrayList[n+1];
		for(int i=0;i<=n;i++){
			graph[i]=new ArrayList<>();
		}
		for(int i=0;i<m;i++){
			int u=I(),v=I();
			graph[u].add(v);
			graph[v].add(u);
		}
	}
	public static int BS(long a[],long x,int ii,int jj)
	{
		// int n=a.length;
		int mid=0;
		int i=ii,j=jj;
		while(i<=j)
		{
			mid=(i+j)/2;
			if(a[mid]<x){
				i=mid+1;
			}else if(a[mid]>x){
				j=mid-1;
			}else{
				return mid;
			}
		}
		return -1;
	}

	//LOWER_BOUND and UPPER_BOUND functions

	public static int lower_bound(long arr[],int start, int end, long X)   //start=0,end=n-1
	{
		if(arr[arr.length-1]<X)return end;
		if(arr[0]>X)return -1;
		int left=start,right=end;
		while(left<right){
			int mid=(left+right)/2;
			if(arr[mid]==X){                                      //Returns last index of lower bound value.
				if(mid<end && arr[mid+1]==X){
					left=mid+1;
				}else{
					return mid;
				}
			}
			// if(arr[mid]==X){                                   //Returns first index of lower bound value.
			// 	if(mid>start && arr[mid-1]==X){
			// 		right=mid-1;
			// 	}else{
			// 		return mid;
			// 	}
			// }
			else if(arr[mid]>X){
				if(mid>start && arr[mid-1]<X){
					return mid-1;
				}else{
					right=mid-1;
				}
			}else{
				if(mid<end && arr[mid+1]>X){
					return mid;
				}else{
					left=mid+1;
				}
			}
		}
		return left;
	}
	public static int upper_bound(long arr[],int start,int end,long X)			//start=0,end=n-1
	{
		if(arr[0]>=X)return start;
		if(arr[arr.length-1]<X)return -1;
		int left=start,right=end;
		while(left<right){
			int mid=(left+right)/2;
			if(arr[mid]==X){                                   //returns first index of upper bound value.
				if(mid>start && arr[mid-1]==X){
					right=mid-1;
				}else{
					return mid;
				}
			}
			// if(arr[mid]==X){									//returns last index of upper bound value.
			// 	if(mid<end && arr[mid+1]==X){
			// 		left=mid+1;
			// 	}else{
			// 		return mid;
			// 	}
			// }
			else if(arr[mid]>X){
				if(mid>start && arr[mid-1]<X){
					return mid;
				}else{
					right=mid-1;
				}
			}else{
				if(mid<end && arr[mid+1]>X){
					return mid+1;
				}else{
					left=mid+1;
				}
			}
		}
		return left;
	}

	//END

	public static boolean isSorted(int a[])
	{
		int n=a.length;
		for(int i=0;i<n-1;i++){
			if(a[i]>a[i+1])return false;
		}
		return true;
	}
	public static boolean isSorted(long a[])
	{
		int n=a.length;
		for(int i=0;i<n-1;i++){
			if(a[i]>a[i+1])return false;
		}
		return true;
	}
	public static int computeXOR(int n) //compute XOR of all numbers between 1 to n.
    {
        if (n % 4 == 0)
            return n;
        if (n % 4 == 1)
            return 1;
        if (n % 4 == 2)
            return n + 1;
        return 0;
    }
	public static ArrayList<Integer> primeSieve(int n)
	{
	    ArrayList<Integer> arr=new ArrayList<>();
	    boolean prime[] = new boolean[n + 1];
        for (int i = 0; i <= n; i++)
        prime[i] = true;
        for (int p = 2; p * p <= n; p++)
        {
            if (prime[p] == true)
            {
                for (int i = p * p; i <= n; i += p)
                prime[i] = false;
            }
        }
        for (int i = 2; i <= n; i++)
        {
            if (prime[i] == true)
            arr.add(i);
        }
        return arr;
	}

	// Fenwick / BinaryIndexed  Tree  USE IT - FenwickTree ft1=new FenwickTree(n);
	public static class FenwickTree
	{
		int farr[];
		int n;
		public FenwickTree(int c)
		{
			n=c+1;
			farr=new int[n];
		}
		// public void update_range(int l,int r,long p)
		// {
		// 	update(l,p);
		// 	update(r+1,(-1)*p);
		// }
		public void update(int x,int p)
		{
			for(;x<n;x+=x&(-x))
			{
				farr[x]+=p;
			}
		}
		public long get(int x)
		{
			long ans=0;
			for(;x>0;x-=x&(-x))
			{
				ans=ans+farr[x];
			}
			return ans;
		}
	}
	//Disjoint Set Union
	public static class DSU
	{
	    int par[],rank[];
	    public DSU(int c)
	    {
	        par=new int[c+1];
	        rank=new int[c+1];
	        for(int i=0;i<=c;i++)
	        {
	            par[i]=i;
	            rank[i]=0;
	        }
	    }
	    public int find(int a)
	    {
	        if(a==par[a])
	        return a;
	        return par[a]=find(par[a]);
	    }
	    public void union(int a,int b)
	    {
	        int a_rep=find(a),b_rep=find(b);
	        if(a_rep==b_rep)
	        return;
	        if(rank[a_rep]<rank[b_rep])
	        par[a_rep]=b_rep;
	        else if(rank[a_rep]>rank[b_rep])
	        par[b_rep]=a_rep;
	        else
	        {
	            par[b_rep]=a_rep;
	            rank[a_rep]++;
	        }
	    }
	}
	
    public static class myComp1 implements Comparator<pair1>
    {
		//sort in ascending order.
    	public int compare(pair1 p1,pair1 p2)
    	{
    	    if(p1.a==p2.a)
    	    return 0;
    	    else if(p1.a<p2.a)
    	    return -1;
    	    else
    	    return 1;
    	}
		//sort in descending order.
		// public int compare(pair p1,pair p2)
    	// {
    	//     if(p1.a==p2.a)
    	//     return 0;
    	//     else if(p1.a<p2.a)
    	//     return 1;
    	//     else
    	//     return -1;
    	// }
    }
	public static class pair1
    {
    	long a;
    	long b;
    	public pair1(long val,long index)
    	{
    	    a=val;
    	    b=index;
    	}
    }
    public static ArrayList<pair1> mergeIntervals(ArrayList<pair1> arr)
	{
	    //****************use this in main function-Collections.sort(arr,new myComp1());
	    ArrayList<pair1> a1=new ArrayList<>();
	    if(arr.size()<=1)
	    return arr;
	    a1.add(arr.get(0));
	    int i=1,j=0;
	    while(i<arr.size())
	    {
	        if(a1.get(j).b<arr.get(i).a)
	        {
	           a1.add(arr.get(i));
	           i++;
	           j++;
	        }
	        else if(a1.get(j).b>arr.get(i).a && a1.get(j).b>=arr.get(i).b)
	        {
	            i++;
	        }
	        else if(a1.get(j).b>=arr.get(i).a)
	        {
	            long a=a1.get(j).a;
	            long b=arr.get(i).b;
	            a1.remove(j);
	            a1.add(new pair1(a,b));
	            i++;
	        }
	    }
	    return a1;
	}
	public static ArrayList<Long> primeFact(long a)
	{
	    ArrayList<Long> arr=new ArrayList<>();
	    while(a%2==0){
	        arr.add(2L);
	        a=a/2;
	    }
	    for(long i=3;i*i<=a;i+=2){
	        while(a%i==0){
	            arr.add(i);
	            a=a/i;
	        }
	    }
	    if(a>2)arr.add(a);
	    return arr;
	}
	public static boolean isInteger(double N)
	{
		int X = (int)N;
		double temp2 = N - X;
		if (temp2 > 0)
		{
			return false;
		}
		return true;
	}
	public static boolean isPalindrome(String s,int n)
	{
		for(int i=0;i<=n/2;i++){
			if(s.charAt(i)!=s.charAt(n-i-1)){
				return false;
			}
		}
		return true;
	}
	public static int gcd(int a,int b)
	{
	    if(b==0)
	    return a;
	    else
	    return gcd(b,a%b);
	}
	public static long gcd(long a,long b)
	{
	    if(b==0)
	    return a;
	    else
	    return gcd(b,a%b);
	}
	public static long fact(long n)
	{
		long fact=1;
		for(long i=2;i<=n;i++){
			fact=((fact%mod)*(i%mod))%mod;
		}
		return fact;
	}
	public static long fact(int n)
	{
		long fact=1;
		for(int i=2;i<=n;i++){
			fact=((fact%mod)*(i%mod))%mod;
		}
		return fact;
	} 
	public static boolean isPrime(int n) 
	{ 
	    if (n <= 1) 
	        return false; 
	    if (n <= 3) 
	        return true; 
	    if (n % 2 == 0 || n % 3 == 0) 
	        return false; 
	    double sq=Math.sqrt(n);
	  
	    for (int i = 5; i <= sq; i = i + 6) 
	        if (n % i == 0 || n % (i + 2) == 0) 
	            return false; 
	    return true; 
	} 
    public static boolean isPrime(long n) 
	{ 
	    if (n <= 1) 
	        return false; 
	    if (n <= 3) 
	        return true; 
	    if (n % 2 == 0 || n % 3 == 0) 
	        return false; 
	    double sq=Math.sqrt(n);
	
	    for (int i = 5; i <= sq; i = i + 6) 
	        if (n % i == 0 || n % (i + 2) == 0) 
	            return false; 
	    return true; 
	}
	public static void printArray(long a[])
	{
		for(int i=0;i<a.length;i++){
			out.print(a[i]+" ");
		}
		out.println();
	}
	public static void printArray(int a[])
	{
		for(int i=0;i<a.length;i++){
			out.print(a[i]+" ");
		}
		out.println();
	}
	public static void printArray(char a[])
	{
		for(int i=0;i<a.length;i++){
			out.print(a[i]);
		}
		out.println();
	}
	public static void printArray(String a[])
	{
		for(int i=0;i<a.length;i++){
			out.print(a[i]+" ");
		}
		out.println();
	}
	public static void printArray(boolean a[])
	{
		for(int i=0;i<a.length;i++){
			out.print(a[i]+" ");
		}
		out.println();
	}
	public static void printArray(pair a[])
	{
		for(pair p:a){
			out.println(p.a+"->"+p.b);
		}
	}
	public static void printArray(int a[][])
	{
		for(int i=0;i<a.length;i++){
			for(int j=0;j<a[i].length;j++){
				out.print(a[i][j]+" ");
			}out.println();
		}
	}
	public static void printArray(long a[][])
	{
		for(int i=0;i<a.length;i++){
			for(int j=0;j<a[i].length;j++){
				out.print(a[i][j]+" ");
			}out.println();
		}
	}
	public static void printArray(char a[][])
	{
		for(int i=0;i<a.length;i++){
			for(int j=0;j<a[i].length;j++){
				out.print(a[i][j]+" ");
			}out.println();
		}
	}
	public static void printArrayL(ArrayList<Long> arr)
	{
		for(int i=0;i<arr.size();i++){
			out.print(arr.get(i)+" ");
		}
		out.println();
	}
	public static void printArrayI(ArrayList<Integer> arr)
	{
		for(int i=0;i<arr.size();i++){
			out.print(arr.get(i)+" ");
		}
		out.println();
	}
	public static void printArrayS(ArrayList<String> arr)
	{
		for(int i=0;i<arr.size();i++){
			out.print(arr.get(i)+" ");
		}
		out.println();
	}
	public static void printMapInt(HashMap<Integer,Integer> hm){
		for(Map.Entry<Integer,Integer> e:hm.entrySet()){
			out.println(e.getKey()+"->"+e.getValue());
		}out.println();
	}
	public static void printMapLong(HashMap<Long,Long> hm){
		for(Map.Entry<Long,Long> e:hm.entrySet()){
			out.println(e.getKey()+"->"+e.getValue());
		}out.println();
	}

	//Modular Arithmetic

	public static long add(long a,long b)
	{
		a+=b;
		if(a>=mod)a-=mod;
		return a;
	}
	public static long sub(long a,long b)
	{
		a-=b;
		if(a<0)a+=mod;
		return a;
	}
	public static long mul(long a,long b)
	{
		return ((a%mod)*(b%mod))%mod;
	}
	public static long divide(long a,long b,long m)
	{
		a=mul(a,modInverse(b,m));
		return a;
	}
	public static long modInverse(long a,long m)
	{
		int x=0,y=0;
		own p=new own(x,y);
		long g=gcdExt(a,m,p);
		if(g!=1){
			out.println("inverse does not exists");
			return -1;
		}else{
			long res=((p.a%m)+m)%m;
			return res;
		}
	}
	public static long gcdExt(long a,long b,own p)
	{
		if(b==0){
			p.a=1;
			p.b=0;
			return a;
		}
		int x1=0,y1=0;
		own p1=new own(x1,y1);
		long gcd=gcdExt(b,a%b,p1);
		p.b=p1.a - (a/b) * p1.b;
		p.a=p1.b;
		return gcd;
	}
	public static long pwr(long m,long n)
	{
		long res=1;
		if(m==0)
		return 0;
		while(n>0)
		{
			if((n&1)!=0)
			{
				res=(res*m);
			}
			n=n>>1;
			m=(m*m);
		}
		return res;
	}
	public static long modpwr(long m,long n)
	{
		long res=1;
		m=m%mod;
		if(m==0)
		return 0;
		while(n>0)
		{
			if((n&1)!=0)
			{
				res=(res*m)%mod;
			}
			n=n>>1;
			m=(m*m)%mod;
		}
		return res;
	}
	public static class own
    {
    	long a;
    	long b;
    	public own(long val,long index)
    	{
    	    a=val;
    	    b=index;
    	}
    }

	//Modular Airthmetic

	public static void sort(int[] A)
	{
        int n = A.length;
        Random rnd = new Random();
        for(int i=0; i<n; ++i)
		{
            int tmp = A[i];
            int randomPos = i + rnd.nextInt(n-i);
            A[i] = A[randomPos];
            A[randomPos] = tmp;
        }
        Arrays.sort(A);
    }
	public static void sort(char[] A)
	{
        int n = A.length;
        Random rnd = new Random();
        for(int i=0; i<n; ++i)
		{
            char tmp = A[i];
            int randomPos = i + rnd.nextInt(n-i);
            A[i] = A[randomPos];
            A[randomPos] = tmp;
        }
        Arrays.sort(A);
    }
    public static void sort(long[] A)
	{
	    int n = A.length;
        Random rnd = new Random();
        for(int i=0; i<n; ++i)
		{
            long tmp = A[i];
            int randomPos = i + rnd.nextInt(n-i);
            A[i] = A[randomPos];
            A[randomPos] = tmp;
        }
	    Arrays.sort(A);
	}
	public static int I(){return sc.I();}
    public static long L(){return sc.L();}
    public static String S(){return sc.S();}
    public static double D(){return sc.D();}
}
class FastReader {  
    BufferedReader br;
    StringTokenizer st;
    public FastReader(){
        br = new BufferedReader(new InputStreamReader(System.in));
    }
    String next(){
        while (st == null || !st.hasMoreElements()){
            try {
                st = new StringTokenizer(br.readLine());
            }
            catch (IOException e){
                e.printStackTrace();
            }
        }
        return st.nextToken();
    }
    int I(){ 
        return Integer.parseInt(next());
    }
    long L(){ 
        return Long.parseLong(next());
    }
    double D(){
         return Double.parseDouble(next());
    }
    String S(){
        String str = "";
        try 
        {
            str = br.readLine();
        }
        catch (IOException e)
        {
            e.printStackTrace();
        }
        return str;
    }
}
