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 

//Utilities
import java.io.*;
import java.util.*;

public class D {
	static int t;
	static long x, y;
	
	public static void main(String[] args) throws IOException {
		t = in.iscan();
		while (t-- > 0) {
			run();
		}
		out.close();
	} 
	
	static void run() throws IOException {
		x = in.lscan(); y = in.lscan();
		if (y < x) {
			out.println(x + y);
		}
		else {
			out.println((x+y)/2);
		}
	}
	
	static INPUT in = new INPUT(System.in);
	static PrintWriter out = new PrintWriter(System.out);
	private static class INPUT {

		private InputStream stream;
		private byte[] buf = new byte[1024];
		private int curChar, numChars;

		public INPUT (InputStream stream) {
			this.stream = stream;
		}

		public INPUT (String file) throws IOException {
			this.stream = new FileInputStream (file);
		}

		public int cscan () throws IOException {
			if (curChar >= numChars) {
				curChar = 0;
				numChars = stream.read (buf);
			}
			
			if (numChars == -1)
				return numChars;

			return buf[curChar++];
		}

		public int iscan () throws IOException {
			int c = cscan (), sgn = 1;
			
			while (space (c))
				c = cscan ();

			if (c == '-') {
				sgn = -1;
				c = cscan ();
			}

			int res = 0;

			do {
				res = (res << 1) + (res << 3);
				res += c - '0';
				c = cscan ();
			}
			while (!space (c));

			return res * sgn;
		}

		public String sscan () throws IOException {
			int c = cscan ();
			
			while (space (c))
				c = cscan ();

			StringBuilder res = new StringBuilder ();

			do {
				res.appendCodePoint (c);
				c = cscan ();
			}
			while (!space (c));

			return res.toString ();
		}

		public double dscan () throws IOException {
			int c = cscan (), sgn = 1;
			
			while (space (c))
				c = cscan ();

			if (c == '-') {
				sgn = -1;
				c = cscan ();
			}

			double res = 0;

			while (!space (c) && c != '.') {
				if (c == 'e' || c == 'E')
					return res * UTILITIES.fast_pow (10, iscan ());
				
				res *= 10;
				res += c - '0';
				c = cscan ();
			}

			if (c == '.') {
				c = cscan ();
				double m = 1;

				while (!space (c)) {
					if (c == 'e' || c == 'E')
						return res * UTILITIES.fast_pow (10, iscan ());

					m /= 10;
					res += (c - '0') * m;
					c = cscan ();
				}
			}

			return res * sgn;
		}

		public long lscan () throws IOException {
			int c = cscan (), sgn = 1;
			
			while (space (c))
				c = cscan ();

			if (c == '-') {
				sgn = -1;
				c = cscan ();
			}

			long res = 0;

			do {
				res = (res << 1) + (res << 3);
				res += c - '0';
				c = cscan ();
			}
			while (!space (c));

			return res * sgn;
		}

		public boolean space (int c) {
			return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
		}
	}

	public static class UTILITIES {

		static final double EPS = 10e-6;
		
		public static void sort(int[] a, boolean increasing) {
			ArrayList<Integer> arr = new ArrayList<Integer>();
			int n = a.length;
			for (int i = 0; i < n; i++) {
				arr.add(a[i]);
			}
			Collections.sort(arr);
			for (int i = 0; i < n; i++) {
				if (increasing) {
					a[i] = arr.get(i);
				}
				else {
					a[i] = arr.get(n-1-i);
				}
			}
		}
		
		public static void sort(long[] a, boolean increasing) {
			ArrayList<Long> arr = new ArrayList<Long>();
			int n = a.length;
			for (int i = 0; i < n; i++) {
				arr.add(a[i]);
			}
			Collections.sort(arr);
			for (int i = 0; i < n; i++) {
				if (increasing) {
					a[i] = arr.get(i);
				}
				else {
					a[i] = arr.get(n-1-i);
				}
			}
		}
		
		public static void sort(double[] a, boolean increasing) {
			ArrayList<Double> arr = new ArrayList<Double>();
			int n = a.length;
			for (int i = 0; i < n; i++) {
				arr.add(a[i]);
			}
			Collections.sort(arr);
			for (int i = 0; i < n; i++) {
				if (increasing) {
					a[i] = arr.get(i);
				}
				else {
					a[i] = arr.get(n-1-i);
				}
			}
		}

		public static int lower_bound (int[] arr, int x) {
			int low = 0, high = arr.length, mid = -1;

			while (low < high) {
				mid = (low + high) / 2;

				if (arr[mid] >= x)
					high = mid;
				else
					low = mid + 1;
			}

			return low;
		}

		public static int upper_bound (int[] arr, int x) {
			int low = 0, high = arr.length, mid = -1;

			while (low < high) {
				mid = (low + high) / 2;

				if (arr[mid] > x)
					high = mid;
				else
					low = mid + 1;
			}

			return low;
		}
		
		public static void updateMap(HashMap<Integer, Integer> map, int key, int v) {
			if (!map.containsKey(key)) {
				map.put(key, v);
			}
			else {
				map.put(key, map.get(key) + v);
			}
			if (map.get(key) == 0) {
				map.remove(key);
			}
		}

		public static long gcd (long a, long b) {
			return b == 0 ? a : gcd (b, a % b);
		}

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

		public static long fast_pow_mod (long b, long x, int mod) {
			if (x == 0) return 1;
			if (x == 1) return b;
			if (x % 2 == 0) return fast_pow_mod (b * b % mod, x / 2, mod) % mod;

			return b * fast_pow_mod (b * b % mod, x / 2, mod) % mod;
		}

		public static int fast_pow (int b, int x) {
			if (x == 0) return 1;
			if (x == 1) return b;
			if (x % 2 == 0) return fast_pow (b * b, x / 2);

			return b * fast_pow (b * b, x / 2);
		}

		public static long choose (long n, long k) {
			k = Math.min (k, n - k);
			long val = 1;

			for (int i = 0; i < k; ++i)
				val = val * (n - i) / (i + 1);

			return val;
		}

		public static long permute (int n, int k) {
			if (n < k) return 0;
			long val = 1;

			for (int i = 0; i < k; ++i)
				val = (val * (n - i));

			return val;
		}
		
		// start of permutation and lower/upper bound template
		public static void nextPermutation(int[] nums) {
		    //find first decreasing digit
		    int mark = -1;
		    for (int i = nums.length - 1; i > 0; i--) {
		        if (nums[i] > nums[i - 1]) {
		            mark = i - 1;
		            break;
		        }
		    }
		 
		    if (mark == -1) {
		        reverse(nums, 0, nums.length - 1);
		        return;
		    }
		 
		    int idx = nums.length-1;
		    for (int i = nums.length-1; i >= mark+1; i--) {
		        if (nums[i] > nums[mark]) {
		            idx = i;
		            break;
		        }
		    }
		 
		    swap(nums, mark, idx);
		 
		    reverse(nums, mark + 1, nums.length - 1);
		}
		 
		public static void swap(int[] nums, int i, int j) {
		    int t = nums[i];
		    nums[i] = nums[j];
		    nums[j] = t;
		}
		 
		public static void reverse(int[] nums, int i, int j) {
		    while (i < j) {
		        swap(nums, i, j);
		        i++;
		        j--;
		    }
		}
		
		static int lower_bound (int[] arr, int hi, int cmp) {
			int low = 0, high = hi, mid = -1;
			while (low < high) {
				mid = (low + high) / 2;
				if (arr[mid] >= cmp) high = mid;
				else low = mid + 1;
			}
			return low;
		}
	 
		static int upper_bound (int[] arr, int hi, int cmp) {
			int low = 0, high = hi, mid = -1;
			while (low < high) {
				mid = (low + high) / 2;
				if (arr[mid] > cmp) high = mid;
				else low = mid + 1;
			}
			return low;
		}
		// end of permutation and lower/upper bound template
	}
}