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.math.*;
import java.lang.*;

public class ModerateModularMode {
    
    // static int mod = 998244353;
    static int mod = 1000000007;

    public static class Reader {
        final private int BUFFER_SIZE = 1 << 16;
        private DataInputStream din;
        private byte[] buffer;
        private int bufferPointer, bytesRead;
 
        public Reader()
        {
            din = new DataInputStream(System.in);
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }
 
        public Reader(String file_name) throws IOException
        {
            din = new DataInputStream(
                new FileInputStream(file_name));
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }
 
        public String readLine() throws IOException
        {
            byte[] buf = new byte[64]; // line length
            int cnt = 0, c;
            while ((c = read()) != -1) {
                if (c == '\n') {
                    if (cnt != 0) {
                        break;
                    }
                    else {
                        continue;
                    }
                }
                buf[cnt++] = (byte)c;
            }
            return new String(buf, 0, cnt);
        }
 
        public int nextInt() throws IOException
        {
            int ret = 0;
            byte c = read();
            while (c <= ' ') {
                c = read();
            }
            boolean neg = (c == '-');
            if (neg)
                c = read();
            do {
                ret = ret * 10 + c - '0';
            } while ((c = read()) >= '0' && c <= '9');
 
            if (neg)
                return -ret;
            return ret;
        }
 
        public long nextLong() throws IOException
        {
            long ret = 0;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();
            do {
                ret = ret * 10 + c - '0';
            } while ((c = read()) >= '0' && c <= '9');
            if (neg)
                return -ret;
            return ret;
        }
 
        public double nextDouble() throws IOException
        {
            double ret = 0, div = 1;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();
 
            do {
                ret = ret * 10 + c - '0';
            } while ((c = read()) >= '0' && c <= '9');
 
            if (c == '.') {
                while ((c = read()) >= '0' && c <= '9') {
                    ret += (c - '0') / (div *= 10);
                }
            }
 
            if (neg)
                return -ret;
            return ret;
        }
 
        private void fillBuffer() throws IOException
        {
            bytesRead = din.read(buffer, bufferPointer = 0,
                                 BUFFER_SIZE);
            if (bytesRead == -1)
                buffer[0] = -1;
        }
 
        private byte read() throws IOException
        {
            if (bufferPointer == bytesRead)
                fillBuffer();
            return buffer[bufferPointer++];
        }
 
        public void close() throws IOException
        {
            if (din == null)
                return;
            din.close();
        }
    }

    public static void main(String[] args) throws Exception {
        Reader scn = new Reader();
        PrintWriter pw = new PrintWriter(System.out);
        int t = scn.nextInt();
        outer : while(t-->0){
            int x = scn.nextInt();
            int y = scn.nextInt();
            if(x == y){
            	pw.println(x);
            	continue outer;
            }
            if(x > y){
            	pw.println(x+y);
            	continue outer;
            }
            pw.println(y - (y % x)/2);
        }
        pw.close();
    }

    public static class Pair{
        int x;
        int y;

        Pair(int x, int y){
            this.x = x;
            this.y = y;
        }
    }

    private static void sort(int[] arr) {
        List<Integer> list = new ArrayList<>();
        for (int i=0; i<arr.length; i++){
            list.add(arr[i]);
        }
        Collections.sort(list); // collections.sort uses nlogn in backend
        for (int i = 0; i < arr.length; i++){
            arr[i] = list.get(i);
        }
    }

    private static void sort(long[] arr) {
        List<Long> list = new ArrayList<>();
        for(int i=0; i<arr.length; i++){
            list.add(arr[i]);
        }
        Collections.sort(list); // collections.sort uses nlogn in backend
        for (int i = 0; i < arr.length; i++){
            arr[i] = list.get(i);
        }
    }

    // private static void sort(Pair[] arr) {
    //     List<Pair> list = new ArrayList<>();
    //     for(int i=0; i<arr.length; i++){
    //         list.add(arr[i]);
    //     }
    //     Collections.sort(list); // collections.sort uses nlogn in backend
    //     for (int i = 0; i < arr.length; i++){
    //         arr[i] = list.get(i);
    //     }
    // }

    private static void reverseSort(int[] arr){
        List<Integer> list = new ArrayList<>();
        for (int i=0; i<arr.length; i++){
            list.add(arr[i]);
        }
        Collections.sort(list, Collections.reverseOrder()); // collections.sort uses nlogn in backend
        for (int i = 0; i < arr.length; i++){
            arr[i] = list.get(i);
        }
    }

    private static void reverseSort(long[] arr){
        List<Long> list = new ArrayList<>();
        for (int i=0; i<arr.length; i++){
            list.add(arr[i]);
        }
        Collections.sort(list, Collections.reverseOrder()); // collections.sort uses nlogn in backend
        for (int i = 0; i < arr.length; i++){
            arr[i] = list.get(i);
        }
    }

    private static void reverseSort(ArrayList<Integer> list){
        Collections.sort(list, Collections.reverseOrder());
    }

    private static int lowerBound(int[] arr, int x){
        int n = arr.length, si = 0, ei = n - 1;
        while(si <= ei){
            int mid = si + (ei - si)/2;
            if(arr[mid] == x){
                if(mid-1 >= 0 && arr[mid-1] == arr[mid]){
                    ei = mid-1;
                }else{
                    return mid;
                }
            }else if(arr[mid] > x){
                ei = mid - 1; 
            }else{
                si = mid+1;
            }
        }
        return si; 
    }

    private static int upperBound(int[] arr, int x){
        int n = arr.length, si = 0, ei = n - 1;
        while(si <= ei){
            int mid = si + (ei - si)/2;
            if(arr[mid] == x){
                if(mid+1 < n && arr[mid+1] == arr[mid]){
                    si = mid+1;
                }else{
                    return mid + 1;
                }
            }else if(arr[mid] > x){
                ei = mid - 1; 
            }else{
                si = mid+1;
            }
        }
        return si; 
    }

    private static int upperBound(ArrayList<Integer> list, int x){
        int n = list.size(), si = 0, ei = n - 1;
        while(si <= ei){
            int mid = si + (ei - si)/2;
            if(list.get(mid) == x){
                if(mid+1 < n && list.get(mid+1) == list.get(mid)){
                    si = mid+1;
                }else{
                    return mid + 1;
                }
            }else if(list.get(mid) > x){
                ei = mid - 1; 
            }else{
                si = mid+1;
            }
        }
        return si; 
    }

    // (x^y)%p in O(logy)
    private static long power(long x, long y){
        long res = 1; 
        x = x % mod;
        while(y > 0){
            if ((y & 1) == 1){
                res = (res * x) % mod;
            }
            y = y >> 1; 
            x = (x * x) % mod;
        }
        return res;
    }

    public static boolean nextPermutation(int[] arr) {
        if(arr == null || arr.length <= 1){
            return false;
        }
        
        int last = arr.length-2;
        while(last >= 0){
            if(arr[last] < arr[last+1]){
                break;
            }
            last--;
        }

        if (last < 0){
              return false;
        }
        
        if(last >= 0){
            int nextGreater = arr.length-1;
            for(int i=arr.length-1; i>last; i--){
                if(arr[i] > arr[last]){
                    nextGreater = i;
                    break;
                }
            }
            swap(arr, last, nextGreater);
        }
        
        reverse(arr, last+1, arr.length-1);
        return true;
    }
    
    private static void swap(int[] arr, int i, int j){
        int temp = arr[i];
        arr[i] = arr[j];
        arr[j] = temp;
    }
    
    private static void reverse(int[] arr, int i, int j){
        while(i < j){
            swap(arr, i++, j--);
        }
    }

    private static String reverseStr(String s){
        StringBuilder sb = new StringBuilder(s);
        return sb.reverse().toString();
    }

    // TC- O(logmax(a,b))
    private static int gcd(int a, int b) {
        if(a == 0){
            return b;
        }
        return gcd(b%a, a);
    }

    private static long gcd(long a, long b) {
        if(a == 0L){
            return b;
        }
        return gcd(b%a, a);
    }

    private static long lcm(long a, long b) {
        return a / gcd(a, b) * b;
    }

    // TC- O(logmax(a,b))
    private static int lcm(int a, int b) {
        return a / gcd(a, b) * b;
    }

    private static long inv(long x){
        return power(x, mod - 2);
    }

    private static long summation(long n){
        return (n * (n + 1L)) >> 1;
    } 
}