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 

/*
⠀⠀⠀⠀⣠⣶⡾⠏⠉⠙⠳⢦⡀⠀⠀⠀⢠⠞⠉⠙⠲⡀⠀
⠀⠀⠀⣴⠿⠏⠀⠀⠀⠀⠀⠀⢳⡀⠀⡏⠀⠀Y⠀⠀⢷
⠀⠀⢠⣟⣋⡀⢀⣀⣀⡀⠀⣀⡀⣧⠀⢸⠀⠀A⠀⠀ ⡇
⠀⠀⢸⣯⡭⠁⠸⣛⣟⠆⡴⣻⡲⣿⠀⣸⠀⠀S⠀  ⡇
⠀⠀⣟⣿⡭⠀⠀⠀⠀⠀⢱⠀⠀⣿⠀⢹⠀⠀H⠀⠀ ⡇
⠀⠀⠙⢿⣯⠄⠀⠀⠀⢀⡀⠀⠀⡿⠀⠀⡇⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠹⣶⠆⠀⠀⠀⠀⠀⡴⠃⠀⠀⠘⠤⣄⣠⠞⠀
⠀⠀⠀⠀⠀⢸⣷⡦⢤⡤⢤⣞⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⣤⣴⣿⣏⠁⠀⠀⠸⣏⢯⣷⣖⣦⡀⠀⠀⠀⠀⠀⠀
⢀⣾⣽⣿⣿⣿⣿⠛⢲⣶⣾⢉⡷⣿⣿⠵⣿⠀⠀⠀⠀⠀⠀
⣼⣿⠍⠉⣿⡭⠉⠙⢺⣇⣼⡏⠀⠀⠀⣄⢸⠀⠀⠀⠀⠀⠀
⣿⣿⣧⣀⣿………⣀⣰⣏⣘⣆⣀⠀⠀
 */

import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter; // System.out is a PrintStream
import java.util.InputMismatchException;


public class D1604 {
    private static int MOD = (int)1e9 + 7, mod = 99_82_44_353;
    private static double PI = 3.14159265358979323846;

    public static void main(String[] args) throws IOException {
        FasterScanner scn = new FasterScanner();
        PrintWriter out = new PrintWriter(System.out);
        for (int tc = scn.nextInt(); tc > 0; tc--) {
            int X = scn.nextInt(), Y = scn.nextInt();
            //  N - ([N / X] * X) = Y - ([Y / N] * N)
            //  N - Y = [N / X * X] - [Y / N * N]
            out.println(X + Y);
        }
        out.close();
    }

    /* ------------------- Sorting ------------------- */
    private static void ruffleSort(int[] arr) {
        // int N = arr.length;
        // Random rand = new Random();
        // for (int i = 0; i < N; i++) {
        //     int oi = rand.nextInt(N), temp = arr[i];
        //     arr[i] = arr[oi];
        //     arr[oi] = temp;
        // }
        // Arrays.sort(arr);
    }
        
    /* ------------------- Sorting ------------------- */
    
    private static boolean isPalindrome(String str) {
        for (int i = 0, j = str.length() - 1; i < j; i++, j--) {
            if (str.charAt(i) != str.charAt(j)) {
                return false;
            }
        }
        return true;
    }
    
    private static boolean isPalindrome(char[] str) {
        for (int i = 0, j = str.length - 1; i < j; i++, j--) {
            if (str[i] != str[j]) {
                return false;
            }
        }
        return true;
    }
    
    /* ------------------- Pair class ------------------- */
    private static class Pair implements Comparable<Pair> {
		int x, y;
		Pair(int x, int y) {
			this.x = x;
			this.y = y;
		}
		public int compareTo(Pair o) {
			return this.x == o.x ? this.y - o.y : this.x - o.x;
		}
	}

    /* ------------------- HCF and LCM ------------------- */
    private static int gcd(int num1, int num2) {
        int temp = 0;
        while (num2 != 0) {
            temp = num1;
            num1 = num2;
            num2 = temp % num2;
        }
        return num1;
    }
    
    private static int lcm(int num1, int num2) {
        return (int)((1L * num1 * num2) / gcd(num1, num2));
    }
    
    /* ------------------- primes and prime factorization ------------------- */
    private static boolean[] seive(int N) {
        // true means not prime, false means is a prime number :)
        boolean[] notPrimes = new boolean[N + 1];
        notPrimes[0] = notPrimes[1] = true;
        for (int i = 2; i * i <= N; i++) {
            if (notPrimes[i]) continue;
            for (int j = i * i; j <= N; j += i) {
                notPrimes[j] = true;
            }
        }
        return notPrimes;
    }

	/*
    private static TreeMap<Integer, Integer> primeFactors(long N) {
		TreeMap<Integer, Integer> primeFact = new TreeMap<>();
		for (int i = 2; i <= Math.sqrt(N); i++) {
            int count = 0;
            while (N % i == 0) {
                N /= i;
                count++;
            }
            if (count != 0) {
                primeFact.put(i, count);
            }
		}
		if (N != 1) {
            primeFact.put((int)N, 1);
        }
		return primeFact;
	}
    */

    /* ------------------- Binary Search ------------------- */
    private static long factorial(int N) {
        long ans = 1L;
        for (int i = 2; i <= N; i++) {
            ans *= i;
        }
        return ans;
    }

    private static long[] factorialDP(int N) {
        long[] factDP = new long[N + 1];
        factDP[0] = factDP[1] = 1;
        for (int i = 2; i <= N; i++) {
            factDP[i] = factDP[i - 1] * i;
        }
        return factDP;
    }

    private static long factorialMod(int N, int mod) {
        long ans = 1L;
        for (int i = 2; i <= N; i++) {
            ans = ((ans % mod) * (i % mod)) % mod;
        }
        return ans;
    }

    /* ------------------- Binary Search ------------------- */
    private static int floorSearch(int[] arr, int st, int ed, int tar) {
        int ans = -1;
        while (st <= ed) {
            int mid = ((ed - st) >> 1) + st;
            if (arr[mid] <= tar) {
                ans = mid;
                st = mid + 1;
            } else {
                ed = mid - 1;
            }
        }
        return ans;
    }
    
    private static int ceilingSearch(int[] arr, int st, int ed, int tar) {
        int ans = -1;
        while (st <= ed) {
            int mid = ((ed - st) >> 1) + st;
            if (arr[mid] < tar) {
                st = mid + 1;
            } else {
                ans = mid;
                ed = mid - 1;
            }
        }
        return ans;
    }
    
    /* ------------------- Power Function ------------------- */
    public static long pow(long x, long y) {
        long res = 1;
		while (y > 0) {
            if ((y & 1) != 0) {
                res = (res * x);
				y--;
			}
			x = (x * x);
			y >>= 1;
		}
		return res;
	}
    
	public static long powMod(long x, long y, int mod) {
        long res = 1;
		while (y > 0) {
            if ((y & 1) != 0) {
                res = (res * x) % mod;
				y--;
			}
			x = (x * x) % mod;
			y >>= 1;
		}
		return res % mod;
	}

    /* ------------------- Disjoint Set(Union and Find) ------------------- */
    private static class DSU {
		public int[] parent, rank;
		DSU(int N) {
			parent = new int[N];
			rank = new int[N];
			for (int i = 0; i < N; i++) {
				parent[i] = i;
                rank[i] = 1;
            }
		}
		public int find(int a) {
			if (parent[a] == a) {
				return a;
            }
            return parent[a] = find(parent[a]);
		}
		public boolean union(int a, int b) {
			int parA = find(a), parB = find(b);
			if (parA == parB) return false;
			if (rank[parA] > rank[parB]) {
                parent[parB] = parA;
            } else if (rank[parA] < rank[parB]) {
                parent[parA] = parB;
            } else {
                parent[parA] = parB;
                rank[parB]++;
            }
            return true;
		}
	}
    
    /* ------------------- Scanner class for input ------------------- */
    
    private static class FasterScanner {
		private InputStream stream;
		private byte[] buffer = new byte[1024];
		private int curChar, numChars;
		private SpaceCharFilter filter;

		public FasterScanner() {
            // default
			this.stream = System.in;
		}

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

		private int readChar() {
			if (numChars == -1) {
				throw new InputMismatchException();
            }
			if (curChar >= numChars) {
				curChar = 0;
				try {
					numChars = stream.read(buffer);
				} catch (IOException e) {
					throw new InputMismatchException(e.getMessage());
				}
				if (numChars <= 0) {
					return -1;
                }
			}
			return buffer[curChar++];
		}

		private boolean isWhiteSpace(int c) {
			if (filter != null) {
				return filter.isWhiteSpace(c);
            }
			return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
		}

		private boolean isNewLine(int ch) {
			if (filter != null) {
				return filter.isNewLine(ch);
            }
			return ch == '\r' || ch == '\n' || ch == -1;
		}

        public char nextChar() {
            int ch = readChar();
            char res = '\0';
            while (isWhiteSpace(ch)) {
                ch = readChar();
            }
            do {
                res = (char)ch;
                ch = readChar();
            } while (!isWhiteSpace(ch));
            return res;
        }

		public String next() {
			int ch = readChar();
            StringBuilder res = new StringBuilder();
			while (isWhiteSpace(ch)) {
				ch = readChar();
            }
			do {
				res.appendCodePoint(ch);
				ch = readChar();
			} while (!isWhiteSpace(ch));
			return res.toString();
		}

		public String nextLine() {
			int ch = readChar();
            StringBuilder res = new StringBuilder();
			do {
				res.appendCodePoint(ch);
				ch = readChar();
			} while (!isNewLine(ch));
			return res.toString();
		}

		public int nextInt() {
			int ch = -1, sgn = 1, res = 0;
            do {
                ch = readChar();
            } while (isWhiteSpace(ch));
			if (ch == '-') {
				sgn = -1;
				ch = readChar();
			}
			do {
				if (ch < '0' || ch > '9') {
					throw new InputMismatchException("not a number");
                }
				res = (res * 10) + (ch - '0');
				ch = readChar();
			} while (!isWhiteSpace(ch));
            
			return res * sgn;
		}

		public long nextLong() {
			int ch = -1, sgn = 1;
            long res = 0L;
            do {
                ch = readChar();
            } while (isWhiteSpace(ch));
			if (ch == '-') {
				sgn = -1;
				ch = readChar();
			}
			do {
				if (ch < '0' || ch > '9') {
					throw new InputMismatchException("not a number");
                }
				res = (10L * res) + (ch - '0');
				ch = readChar();
			} while (!isWhiteSpace(ch));

			return 1L * res * sgn;
		}

        public double nextDouble() {
            return Double.parseDouble(next());
        }

        /* for custom delimiters */
		public interface SpaceCharFilter {
			public boolean isWhiteSpace(int ch);
			public boolean isNewLine(int ch);
		}
	}
}
