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.IOException;
import java.io.InputStreamReader;
import java.util.*;
 
public class Solution{
static FastScanner sc = new FastScanner();
public static void solve(){
     long x=sc.nextLong();
     long y=sc.nextLong();
     long l=1,r=(long)1e18;
     if (x>y) 
      System.out.println(x+y);
    else
      System.out.println((x+y)/2l);
    


    }

public static void main(String[] args) {
  int t = sc.nextInt();
  // int t=1;
  outer: for (int tt = 0; tt < t; tt++) {
    solve();
  }

}
static boolean isPrime(int n)
    {
        if (n <= 1)
            return false;
        if (n <= 3)
            return true;
  
        if (n % 2 == 0 || n % 3 == 0)
            return false;
  
        for (int i = 5; i * i <= n; i = i + 6)
            if (n % i == 0 || n % (i + 2) == 0)
                return false;
  
        return true;
    }
public static int[] LPS(String s){
  int[] lps=new int[s.length()];
  int i=0,j=1;
  while (j<s.length()) {
    if(s.charAt(i)==s.charAt(j)){
      lps[j]=i+1;
      i++;
      j++;
      continue;
    }else{
      if (i==0) {
        j++;
        continue;
      }
      i=lps[i-1];
      while(s.charAt(i)!=s.charAt(j) && i!=0) {
        i=lps[i-1];
      }
      if(s.charAt(i)==s.charAt(j)){
      lps[j]=i+1;
      i++;
      }
      j++;
    }
  }
  return lps;
}
static long getPairsCount(int n, double sum,int[] arr)
    {
        HashMap<Double, Integer> hm = new HashMap<>();
        for (int i = 0; i < n; i++) {
            if (!hm.containsKey((double)arr[i]))
                hm.put((double)arr[i], 0);
            hm.put((double)arr[i], hm.get((double)arr[i]) + 1);
        }
        long twice_count = 0;
        for (int i = 0; i < n; i++) {
            if (hm.get(sum - arr[i]) != null)
                twice_count += hm.get(sum - arr[i]);
            if (sum - (double)arr[i] == (double)arr[i])
                twice_count--;
        }
        return twice_count / 2l;
    }
static boolean[] sieveOfEratosthenes(int n)
    {
        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;
            }
        }
        return prime;
 }
static long power(long x, long y, long p)
  {
    long res = 1l; 
    x = x % p;
    if (x == 0)
      return 0;
    while (y > 0)
    {

      if ((y & 1) != 0)
        res = (res * x) % p;
      y>>=1;
      x = (x * x) % p;
    }
    return res;
  }

public static int log2(int N)
    {
        int result = (int)(Math.log(N) / Math.log(2));
  
        return result;
    }

////////////////////////////////////////////////////////////////////////////////////
////////////////////DO NOT READ AFTER THIS LINE //////////////////////////////////
////////////////////////////////////////////////////////////////////////////////////
static long modFact(int n, 
                       int p) 
    { 
        if (n >= p) 
            return 0; 
      
        long result = 1l; 
        for (int i = 3; i <= n; i++) 
            result = (result * i) % p; 
      
        return result; 
    } 
      
static boolean isPalindrom(char[] arr, int i, int j) {
  boolean ok = true;
  while (i <= j) {
    if (arr[i] != arr[j]) {
      ok = false;
      break;
    }
    i++;
    j--;
  }
  return ok;
}

static int max(int a, int b) {
  return Math.max(a, b);
}

static int min(int a, int b) {
  return Math.min(a, b);
}

static long max(long a, long b) {
  return Math.max(a, b);
}

static long min(long a, long b) {
  return Math.min(a, b);
}

static int abs(int a) {
  return Math.abs(a);
}

static long abs(long a) {
  return Math.abs(a);
}

static void swap(long arr[], int i, int j) {
  long temp = arr[i];
  arr[i] = arr[j];
  arr[j] = temp;
}

static void swap(int arr[], int i, int j) {
  int temp = arr[i];
  arr[i] = arr[j];
  arr[j] = temp;
}

static int maxArr(int arr[]) {
  int maxi = Integer.MIN_VALUE;
  for (int x : arr)
    maxi = max(maxi, x);
  return maxi;
}

static int minArr(int arr[]) {
  int mini = Integer.MAX_VALUE;
  for (int x : arr)
    mini = min(mini, x);
  return mini;
}

static long maxArr(long arr[]) {
  long maxi = Long.MIN_VALUE;
  for (long x : arr)
    maxi = max(maxi, x);
  return maxi;
}

static long minArr(long arr[]) {
  long mini = Long.MAX_VALUE;
  for (long x : arr)
    mini = min(mini, x);
  return mini;
}
static int lcm(int a,int b){
  return (int)(((long)a*b)/(long)gcd(a,b));
}
static int gcd(int a, int b) {
  if (b == 0)
    return a;
  return gcd(b, a % b);
}

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

static void ruffleSort(int[] a) {
  int n = a.length;
  Random r = new Random();
  for (int i = 0; i < a.length; i++) {
    int oi = r.nextInt(n);
    int temp = a[i];
    a[i] = a[oi];
    a[oi] = temp;
  }
  Arrays.sort(a);
}

public static int binarySearch(int a[], int target) {
  int left = 0;
  int right = a.length - 1;
  int mid = (left + right) / 2;
  int i = 0;
  while (left <= right) {
    if (a[mid] <= target) {
      i = mid + 1;
      left = mid + 1;
    } else {
      right = mid - 1;
    }
    mid = (left + right) / 2;
  }
  return i-1;
}


static class FastScanner {
  BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
  StringTokenizer st = new StringTokenizer("");

  String next() {
    while (!st.hasMoreTokens())
      try {
        st = new StringTokenizer(br.readLine());
      } catch (IOException e) {
        e.printStackTrace();
      }
    return st.nextToken();
  }

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

  int[] readArray(int n) {
    int[] a = new int[n];
    for (int i = 0; i < n; i++)
      a[i] = nextInt();
    return a;
  }

  long[] readLongArray(int n) {
    long[] a = new long[n];
    for (int i = 0; i < n; i++)
      a[i] = nextLong();
    return a;
  }

  int[][] read2dArray(int n, int m) {
    int arr[][] = new int[n][m];
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < m; j++) {
        arr[i][j] = nextInt();
      }
    }
    return arr;
  }

  ArrayList<Integer> readArrayList(int n) {
    ArrayList<Integer> arr = new ArrayList<Integer>();
    for (int i = 0; i < n; i++) {
      int a = nextInt();
      arr.add(a);
    }
    return arr;
  }

  long nextLong() {
    return Long.parseLong(next());
  }
}
 static class Pair {
  int l, r;

  Pair(int fr, int sc) {
    this.l = fr;
    this.r = sc;
  }
}
}