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 

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import os
import sys
from io import BytesIO, IOBase
#-----------------------IMPORTANT  FUNCTIONS ---------------------------------#
from math import cos, pi, ceil, pi, tan, floor, gcd, sqrt, log2, factorial, log10
from collections import Counter
from copy import deepcopy
from string import ascii_lowercase, ascii_uppercase
from statistics import mean, median, mode
from bisect import *

alpha = ascii_lowercase
beta = ascii_uppercase


#-----------------------NEXT POWER OF 2---------------------------------------#
def nextPowerOf2(n):
    p = 1
    if (n and not (n & (n - 1))):
        return n
    while (p < n):
        p <<= 1
    return p
#-----------------------COMPOSITE  CHECK---------------------------------------#
def isComposite(n):
    if (n <= 1):
        return False
    if (n <= 3):
        return False
    if (n % 2 == 0 or n % 3 == 0):
        return True
    i = 5
    while(i * i <= n):
        if (n % i == 0 or n % (i + 2) == 0):
            return True
        i = i + 6
    return False


#-----------------------GET DIVISORS 1 TO <=N   ------------------------------#
def get_Divisors(n):
    arr = []
    i = 1
    while i <= sqrt(n):
        if (n % i == 0):
            if (n / i == i):
                arr.append(i)
            else:
                arr.append(i)
                arr.append(n // i)
        i = i + 1

    return arr


#----------------------CHECK    PRIMES-----------------------------------#
def isprime(n):
    if n == 1:
        return 0
    i = 2
    while (i * i <= n):
        if (n % i == 0):
            return 0
        i += 1
    return 1


#-----------------------PRE COMPUTED  PRIMES-----------------------------------#
def Sieve(n):
    prime = [True for i in range(n + 1)]
    prime[0] = False
    prime[1] = False
    p = 2
    while (p * p <= n):
        if (prime[p] == True):
            for i in range(p * p, n + 1, p):
                prime[i] = False
        p += 1
    return prime


#-----------------------LARGER VALUE OF  X,Y,10**9+7 --------------------------#
def power(x, y, p):
    res = 1
    x = x % p
    if (x == 0):
        return 0
    while (y > 0):
        if ((y & 1) == 1):
            res = (res * x) % p
        y = y >> 1
        x = (x * x) % p
    return res


#-----------------------       CREATE MATRIX         --------------------------#
def create_matrix(n, m):
    mat = [[] for i in range(n)]
    for i in range(n):
        for j in range(m):
            mat[i].append(0)
    return mat


#By Default Counter stores the value in decending orderCounter({4: 2, 8: 2, 2: 1, 9: 1}
#s=sorted(s.items(),key=lambda k:(k[0],k[1])) ---> [(2, 1), (4, 2), (8, 2), (9, 1)]
#sort 2nd value  from bada se chhota  then(4,2)(8,2)->>(8,2)(4,2) s=sorted(s.items(),key=lambda k:(-k[1],-k[0]))  [(8, 2), (4, 2), (9, 1), (2, 1)]
#for list pair in a list    s.sort(key=lambda k:(-k[1],-k[0])) [[3, 4], [8, 2], [4, 2]]
# from functools import cmp_to_key
#how to use compare ----ss = sorted(s, key=cmp_to_key(compare))
#-----------------------*****CODE STARTS  HERE*****--------------------------#

# from queue import Queue
# from random import *
def main():
    for ttt in range(int(input())):
        x,y=map(int,input().split())
        if x>y:
            print(x+y)
        elif x==y:
            print(x)
        else:
            m=y//x 
            mm=m*x 
            print((mm+y)//2)
            
        
            
        
# Region Fast_______io
BUFSIZE = 8192
class FastIO(IOBase):
    newlines = 0

    def __init__(self, file):
        self._fd = file.fileno()
        self.buffer = BytesIO()
        self.writable = "x" in file.mode or "r" not in file.mode
        self.write = self.buffer.write if self.writable else None

    def read(self):
        while True:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            if not b:
                break
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
        self.newlines = 0
        return self.buffer.read()

    def readline(self):
        while self.newlines == 0:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            self.newlines = b.count(b"\n") + (not b)
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
        self.newlines -= 1
        return self.buffer.readline()

    def flush(self):
        if self.writable:
            os.write(self._fd, self.buffer.getvalue())
            self.buffer.truncate(0), self.buffer.seek(0)


class IOWrapper(IOBase):
    def __init__(self, file):
        self.buffer = FastIO(file)
        self.flush = self.buffer.flush
        self.writable = self.buffer.writable
        self.write = lambda s: self.buffer.write(s.encode("ascii"))
        self.read = lambda: self.buffer.read().decode("ascii")
        self.readline = lambda: self.buffer.readline().decode("ascii")


#sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
input = lambda: sys.stdin.readline().rstrip("\r\n")
if __name__ == "__main__":
    main()