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.*;
import java.util.*;


public class Practice
{
//	static final long mod=7420738134811L;
	static int mod=998244353;
	static final int size=501;
	static FastReader sc=new FastReader(System.in);
//	static Reader sc=new Reader();
	static  PrintWriter out=new PrintWriter(System.out);
	static long[] factorialNumInverse;
	static long[] naturalNumInverse;	
	static int[] sp;
	static long[] fact;
	static ArrayList<Integer> pr;
	public static void main(String[] args) throws IOException
	{
//		System.setIn(new FileInputStream("input.txt"));
//		System.setOut(new PrintStream("output.txt"));
//		factorial(mod);
//		InverseofNumber(mod);
//		InverseofFactorial(mod);
//		make_seive();
		int t=1;
		t=sc.nextInt();
		while(t-->0)
			solve();
		out.close();
		out.flush();
	}
	static void solve() throws IOException
	{
		int x=sc.nextInt(),y=sc.nextInt();
		if(y%x==0)
			out.println(x);
		else if(x<y)
		{
			int r=(x+y)/2;
			r=r%x;
			y=y-r;
			out.println(y);
		}
		else
			out.println(x+y);
	}
//	{
//		int n=sc.nextInt();
//		int arr[]=new int[n];
//		boolean f=false;
//		for(int i=0;i<n;i++)
//		{
//			arr[i]=sc.nextInt();
//			if(i>0 && arr[i]%(i+2)!=0)
//				f=true;
//		}
//		if(arr[0]%2==0 || !f)
//		{
//			out.println("NO");
//			return;
//		}
//		int shift[]=new int[n];
//		for(int i=n-1;i>=0;i--)
//		{
//			int c=0,st=i+2;
//			while(st>1 && arr[i]%st==0)
//			{
//				c++;
//				st--;
//			}
//			shift[i]=c;
//		}
//		int count=0;
//		for(int i=0;i<n;i++)
//		{
//			if(shift[i]==0)
//				count++;
//			else
//			{
//				if(count<shift[i])
//				{
//					out.println("NO");
//					return;
//				}
//				count++;
//			}
//		}
//		out.println("YES");
//	}
	static class Pair implements Cloneable, Comparable<Pair>
	{
		int x,y;
		Pair(int a,int b)
		{
			this.x=a;
			this.y=b;
		}
		@Override
		public boolean equals(Object obj) 
		{
			if(obj instanceof  Pair)
			{
				Pair p=(Pair)obj;
				return p.x==this.x && p.y==this.y;
			}
			return false;
		}
		@Override
		public int hashCode() 
		{
			return Math.abs(x)+101*Math.abs(y);
		}
		@Override
		public String toString() 
		{
			return "("+x+" "+y+")";
		}
		@Override
		protected Pair clone() throws CloneNotSupportedException {
			return new Pair(this.x,this.y);
		}
		@Override
		public int compareTo(Pair a) 
		{
			int t= this.x-a.x;
			if(t!=0)
				return t;
			else
				return this.y-a.y;
		}
		public void swap()
		{
			this.y=this.y+this.x;
			this.x=this.y-this.x;
			this.y=this.y-this.x;			
		}
	}
	static class Tuple implements Cloneable, Comparable<Tuple>
	{
		int x,y,z;
		Tuple(int a,int b,int c)
		{
			this.x=a;
			this.y=b;
			this.z=c;
		}
		public boolean equals(Object obj) 
		{
			if(obj instanceof  Tuple)
			{
				Tuple p=(Tuple)obj;
				return p.x==this.x && p.y==this.y && p.z==this.z;
			}
			return false;
		}
		@Override
		public String toString() 
		{
			return "("+x+","+y+","+z+")";
		}
		@Override
		protected Tuple clone() throws CloneNotSupportedException {
			return new Tuple(this.x,this.y,this.z);
		}
		@Override
		public int compareTo(Tuple a) 
		{
			int x=this.x-a.x;
			if(x!=0)
				return x;
			return this.y-a.y;
		}
	}
	static void arraySort(int arr[])
	{
		ArrayList<Integer> a=new ArrayList<Integer>();
		for (int i = 0; i < arr.length; i++) {
			a.add(arr[i]);
		}
		Collections.sort(a);
		for (int i = 0; i < arr.length; i++) {
			arr[i]=a.get(i);
		}
	}
	static void arraySort(long arr[])
	{
		ArrayList<Long> a=new ArrayList<Long>();
		for (int i = 0; i < arr.length; i++) {
			a.add(arr[i]);
		}
		Collections.sort(a);
		for (int i = 0; i < arr.length; i++) {
			arr[i]=a.get(i);
		}
	}
	static HashSet<Integer> primeFactors(int n)
	{
		HashSet<Integer> ans=new HashSet<Integer>();
		if(n%2==0)
		{
			ans.add(2);
			while((n&1)==0)
				n=n>>1;
		}
		for(int i=3;i*i<=n;i+=2)
		{
			if(n%i==0)
			{
				ans.add(i);
				while(n%i==0)
					n=n/i;
			}
		}
		if(n!=1)
			ans.add(n);
		return ans;
	}
	static void make_seive()
	{
		sp=new int[size];
		pr=new ArrayList<Integer>();
		for (int i=2; i<size; ++i) {
		    if (sp[i] == 0) {
		        sp[i] = i;
		        pr.add(i);
		    }
		    for (int j=0; j<(int)pr.size() && pr.get(j)<=sp[i] && i*pr.get(j)<size; ++j)
		        sp[i * pr.get(j)] = pr.get(j);
		}
	}
	public static void InverseofNumber(int p)
	{
		naturalNumInverse=new long[size];
	    naturalNumInverse[0] = naturalNumInverse[1] = 1;
	    for(int i = 2; i < size; i++)
	        naturalNumInverse[i] = naturalNumInverse[p % i] * (long)(p - p / i) % p;
	}
	// Function to precompute inverse of factorials
	public static void InverseofFactorial(int p)
	{
		factorialNumInverse=new long[size];
	    factorialNumInverse[0] = factorialNumInverse[1] = 1;
	    // pre-compute inverse of natural numbers
	    for(int i = 2; i < size; i++)
	        factorialNumInverse[i] = (naturalNumInverse[i] * factorialNumInverse[i - 1]) % p;
	}
	// Function to calculate factorial of 1 to 200001
	public static void factorial(int p)
	{
		fact=new long[size];
	    fact[0] = 1;
	    for(int i = 1; i < size; i++)
	        fact[i] = (fact[i - 1] * (long)i) % p;
	}
	 
	// Function to return nCr % p in O(1) time
	public static long Binomial(int N, int R)
	{
		if(R<0)
			return 1;
	    // n C r = n!*inverse(r!)*inverse((n-r)!)
	    long ans = ((fact[N] * factorialNumInverse[R]) % mod * factorialNumInverse[N - R]) % mod;
	    return ans;
	}
	static int findXOR(int x)	//from 0 to x
	{
		if(x<0)
			return 0;
		if(x%4==0)
			return x;
		if(x%4==1)
			return 1;
		if(x%4==2)
			return x+1;
		return 0;
	}
	static boolean isPrime(long x)
	{
		if(x==1)
			return false;
		if(x<=3)
			return true;
		if(x%2==0 || x%3==0)
			return false;
		for(int i=5;i<=Math.sqrt(x);i+=2)
			if(x%i==0)
				return false;
		return true;
	}
	static long gcd(long a,long b)
	{
		return (b==0)?a:gcd(b,a%b);
	}
	static int gcd(int a,int b)
	{
		return (b==0)?a:gcd(b,a%b);
	}
	static class Node
	{
		int vertex,dis=0;
		HashSet<Node> adj;
		Node par;
		Node(int ver)
		{
			vertex=ver;
			dis=Integer.MAX_VALUE;
			adj=new HashSet<Node>();
			par=null;
		}
		@Override
		public String toString() 
		{
			return vertex+" ";
		}
	}
	static class Edge
	{
		Node to;
		int cost;
		Edge(Node t,int c)
		{
			this.to=t;
			this.cost=c;
		}
		@Override
		public String toString() {
			return "("+to.vertex+","+cost+") ";
		}
	}
	static long power(long x, long y)
	  {
		if(x<=0)
			return 1;
	    long res = 1; 
	    x = x % mod; 
	    if (x == 0)
	      return 0; 
	    while (y > 0)
	    {
	    	if ((y & 1) != 0)
	    		res = (res * x) % mod;
	    	
	    	y = y >> 1; // y = y/2
	    	x = (x * x) % mod;
	    }
	    return res;
	  }
	static long binomialCoeff(long n, long k)
    {
		if(n<k)
			return 0;
        long res = 1;
//        if(k>n)
//        	return 0;
        // Since C(n, k) = C(n, n-k)
        if (k > n - k)
            k = n - k;
 
        // Calculate value of
        // [n * (n-1) *---* (n-k+1)] / [k * (k-1) *----* 1]
        for (long i = 0; i < k; ++i) {
            res *= (n - i);
            res /= (i + 1);
        }
 
        return res;
    }
	static class FastReader
	{
        byte[] buf = new byte[2048];
        int index, total;
        InputStream in;
 
        FastReader(InputStream is) 
        {
            in = is;
        }
 
        int scan() throws IOException 
        {
            if (index >= total) {
                index = 0;
                total = in.read(buf);
                if (total <= 0) {
                    return -1;
                }
            }
            return buf[index++];
        }
 
        String next() throws IOException 
        {
            int c;
            for (c = scan(); c <= 32; c = scan());
            StringBuilder sb = new StringBuilder();
            for (; c > 32; c = scan()) {
                sb.append((char) c);
            }
            return sb.toString();
        }
 
        int nextInt() throws IOException 
        {
            int c, val = 0;
            for (c = scan(); c <= 32; c = scan());
            boolean neg = c == '-';
            if (c == '-' || c == '+') {
                c = scan();
            }
            for (; c >= '0' && c <= '9'; c = scan()) {
                val = (val << 3) + (val << 1) + (c & 15);
            }
            return neg ? -val : val;
        }
 
        long nextLong() throws IOException 
        {
            int c;
            long val = 0;
            for (c = scan(); c <= 32; c = scan());
            boolean neg = c == '-';
            if (c == '-' || c == '+') {
                c = scan();
            }
            for (; c >= '0' && c <= '9'; c = scan()) {
                val = (val << 3) + (val << 1) + (c & 15);
            }
            return neg ? -val : val;
        }
    }
	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 void printarray(int arr[])
        {
        	for (int i = 0; i < arr.length; i++)
				System.out.print(arr[i]+" ");
        	System.out.println();
        }
    }
}







