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.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.StringTokenizer;
import java.util.*;
import java.io.*;
public class Main {
    // Graph
    // prefix sums
    //inputs
    public static void main(String args[])throws Exception{
        Input sc=new Input();
        precalculates p=new precalculates();
        StringBuilder sb=new StringBuilder();
        int t=sc.readInt();
        for(int f=0;f<t;f++){
            long d[]=sc.readArrayLong();
            long x=d[0],y=d[1];
            x=Math.min(d[0],d[1]);
            y=Math.max(d[0],d[1]);

            long l=x,r=y;
            long n=l+r;
            n/=2;
            while((n%x)!=(y%n)){
                n=l+r;
                n/=2;
                if(Math.abs(n-n%x)>Math.abs(n-y%n)){
                    l=n+1;
                }else if(Math.abs(n-n%x)<Math.abs(n-y%n)){
                    r=n-1;
                }else
                    break;
               // System.out.println(n);
               // System.out.println(n);
               // System.out.println((n%x)+" "+(y%n));
            }
            //System.out.println(n);
            //System.out.println((n%x)+" "+(y%n));
            sb.append(n+"\n");
        }
        System.out.print(sb);
    }
}
class Input{
    BufferedReader br;
    StringTokenizer st;
    Input(){
        br=new BufferedReader(new InputStreamReader(System.in));
        st=new StringTokenizer("");
    }
    public int[] readArray() throws Exception{
        st=new StringTokenizer(br.readLine());
        int a[]=new int[st.countTokens()];
        for(int i=0;i<a.length;i++){
            a[i]=Integer.parseInt(st.nextToken());
        }
        return a;
    }
    public long[] readArrayLong() throws Exception{
        st=new StringTokenizer(br.readLine());
        long a[]=new long[st.countTokens()];
        for(int i=0;i<a.length;i++){
            a[i]=Long.parseLong(st.nextToken());
        }
        return a;
    }
    public int readInt() throws Exception{
        st=new StringTokenizer(br.readLine());
        return Integer.parseInt(st.nextToken());
    }
    public long readLong() throws Exception{
        st=new StringTokenizer(br.readLine());
        return Long.parseLong(st.nextToken());
    }
    public String readString() throws Exception{
        return br.readLine();
    }
    public int[][] read2dArray(int n,int m)throws Exception{
        int a[][]=new int[n][m];
        for(int i=0;i<n;i++){
            st=new StringTokenizer(br.readLine());
            for(int j=0;j<m;j++){
                a[i][j]=Integer.parseInt(st.nextToken());
            }
        }
        return a;
    }
}
class precalculates{
    public int[] prefixSumOneDimentional(int a[]){
        int n=a.length;
        int dp[]=new int[n];
        for(int i=0;i<n;i++){
            if(i==0)
                dp[i]=a[i];
            else
                dp[i]=dp[i-1]+a[i];
        }
        return dp;
    }
    public int[] postSumOneDimentional(int a[]) {
        int n = a.length;
        int dp[] = new int[n];
        for (int i = n - 1; i >= 0; i--) {
            if (i == n - 1)
                dp[i] = a[i];
            else
                dp[i] = dp[i + 1] + a[i];
        }
        return dp;
    }
    public int[][] prefixSum2d(int a[][]){
        int n=a.length;int m=a[0].length;
        int dp[][]=new int[n+1][m+1];
        for(int i=1;i<=n;i++){
            for(int j=1;j<=m;j++){
                dp[i][j]=a[i-1][j-1]+dp[i-1][j]+dp[i][j-1]-dp[i-1][j-1];
            }
        }
        return dp;
    }
    public long pow(long a,long b){
        long mod=1000000007;
        long ans=0;
        if(b<=0)
            return 1;
        if(b%2==0){
            ans=pow(a,b/2)%mod;
            return ((ans%mod)*(ans%mod))%mod;
        }else{
            return ((a%mod)*(ans%mod))%mod;
        }
    }

}
class GraphInteger{
    HashMap<Integer,vertex> vtces;
    class vertex{
        HashMap<Integer,Integer> children;
        public vertex(){
            children=new HashMap<>();
        }
    }
    public GraphInteger(){
        vtces=new HashMap<>();
    }
    public void addVertex(int a){
        vtces.put(a,new vertex());
    }
    public void addEdge(int a,int b,int cost){
        if(!vtces.containsKey(a)){
            vtces.put(a,new vertex());
        }
        if(!vtces.containsKey(b)){
            vtces.put(b,new vertex());
        }
        vtces.get(a).children.put(b,cost);
//        vtces.get(b).children.put(a,cost);
    }
    public boolean isCyclicDirected(){
        boolean isdone[]=new boolean[vtces.size()+1];
        boolean check[]=new boolean[vtces.size()+1];
        for(int i=1;i<=vtces.size();i++) {
            if (!isdone[i] && isCyclicDirected(i,isdone, check)) {
                return true;
            }
        }
        return false;
    }
    private boolean isCyclicDirected(int i,boolean isdone[],boolean check[]){
        if(check[i])
            return true;
        if(isdone[i])
            return false;
        check[i]=true;
        isdone[i]=true;
        Set<Integer> set=vtces.get(i).children.keySet();
        for(Integer ii:set){
            if(isCyclicDirected(ii,isdone,check))
                return true;
        }
        check[i]=false;
        return false;
    }
}




