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 bisect
import heapq
import math
import collections
import sys
import copy
from functools import reduce
import decimal
from io import BytesIO, IOBase
import os
import itertools
import functools
from types import GeneratorType

#
# sys.setrecursionlimit(10 ** 9)
decimal.getcontext().rounding = decimal.ROUND_HALF_UP

graphDict = collections.defaultdict

queue = collections.deque


################## pypy deep recursion handling ##############
# Author = @pajenegod
def bootstrap(f, stack=[]):
    def wrappedfunc(*args, **kwargs):
        to = f(*args, **kwargs)
        if stack:
            return to
        else:
            while True:
                if type(to) is GeneratorType:
                    stack.append(to)
                    to = next(to)
                else:
                    stack.pop()
                    if not stack:
                        return to
                    to = stack[-1].send(to)

    return wrappedfunc


################## Graphs ###################
class Graphs:
    def __init__(self):
        self.graph = graphDict(set)

    def add_edge(self, u, v):
        self.graph[u].add(v)
        self.graph[v].add(u)

    def dfs_utility(self, nodes, visited_nodes, colors, parity, level):
        global count
        if nodes == 1:
            colors[nodes] = -1
        else:
            if len(self.graph[nodes]) == 1 and parity % 2 == 0:
                if q == 1:
                    colors[nodes] = 1
                else:
                    colors[nodes] = -1
                    count += 1
            else:
                if parity % 2 == 0:
                    colors[nodes] = -1
                else:
                    colors[nodes] = 1
        visited_nodes.add(nodes)
        for neighbour in self.graph[nodes]:
            new_level = level + 1
            if neighbour not in visited_nodes:
                self.dfs_utility(neighbour, visited_nodes, colors, level - 1, new_level)

    def dfs(self, node):
        Visited = set()
        color = collections.defaultdict()
        self.dfs_utility(node, Visited, color, 0, 0)
        return color

    def bfs(self, node, f_node):
        count = float("inf")
        visited = set()
        level = 0
        if node not in visited:
            queue.append([node, level])
            visited.add(node)
        flag = 0
        while queue:
            parent = queue.popleft()
            if parent[0] == f_node:
                flag = 1
                count = min(count, parent[1])
            level = parent[1] + 1
            for item in self.graph[parent[0]]:
                if item not in visited:
                    queue.append([item, level])
                    visited.add(item)
        return count if flag else -1
        return False


################### Tree Implementaion ##############
class Tree:
    def __init__(self, data):
        self.data = data
        self.left = None
        self.right = None


def inorder(node, lis):
    if node:
        inorder(node.left, lis)
        lis.append(node.data)
        inorder(node.right, lis)
    return lis


def leaf_node_sum(root):
    if root is None:
        return 0
    if root.left is None and root.right is None:
        return root.data
    return leaf_node_sum(root.left) + leaf_node_sum(root.right)


def hight(root):
    if root is None:
        return -1
    if root.left is None and root.right is None:
        return 0
    return max(hight(root.left), hight(root.right)) + 1


################## Union Find #######################
class UF:
    """An implementation of union find data structure.
    It uses weighted quick union by rank with path compression.
    """

    def __init__(self, N):
        """Initialize an empty union find object with N items.

        Args:
            N: Number of items in the union find object.
        """

        self._id = list(range(N))
        self._count = N
        self._rank = [0] * N

    def find(self, p):
        """Find the set identifier for the item p."""

        id = self._id
        while p != id[p]:
            p = id[p]  # Path compression using halving.
        return p

    def count(self):
        """Return the number of items."""

        return self._count

    def connected(self, p, q):
        """Check if the items p and q are on the same set or not."""

        return self.find(p) == self.find(q)

    def union(self, p, q):
        """Combine sets containing p and q into a single set."""

        id = self._id
        rank = self._rank

        i = self.find(p)
        j = self.find(q)
        if i == j:
            return

        self._count -= 1
        if rank[i] < rank[j]:
            id[i] = j
        elif rank[i] > rank[j]:
            id[j] = i
        else:
            id[j] = i
            rank[i] += 1

    def add_roads(self):
        return set(self._id)

    def __str__(self):
        """String representation of the union find object."""
        return " ".join([str(x) for x in self._id])

    def __repr__(self):
        """Representation of the union find object."""
        return "UF(" + str(self) + ")"


#################################################

def rounding(n):
    return int(decimal.Decimal(f'{n}').to_integral_value())


def factors(n):
    return set(reduce(list.__add__,
                      ([i, n // i] for i in range(1, int(n ** 0.5) + 1) if n % i == 0)))


def p_sum(array):
    return list(itertools.accumulate(array))


def base_change(nn, bb):
    if nn == 0:
        return [0]
    digits = []
    while nn:
        digits.append(int(nn % bb))
        nn //= bb
    return digits[::-1]


def diophantine(a: int, b: int, c: int):
    d, x, y = extended_gcd(a, b)
    r = c // d
    return r * x, r * y


@bootstrap
def extended_gcd(a: int, b: int):
    if b == 0:
        d, x, y = a, 1, 0
    else:
        (d, p, q) = yield extended_gcd(b, a % b)
        x = q
        y = p - q * (a // b)

    yield d, x, y


######################################################################################

'''
Knowledge and awareness are vague, and perhaps better called illusions.
Everyone lives within their own subjective interpretation.
                                                            ~Uchiha Itachi
'''

################################ <fast I/O> ###########################################
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, **kwargs):
        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)


#############################################<I/O Region >##############################################


def inp():
    return sys.stdin.readline().strip()


def map_inp(v_type):
    return map(v_type, inp().split())


def list_inp(v_type):
    return list(map_inp(v_type))


######################################## Solution ####################################


for _ in range(int(inp())):
    x, y = map_inp(int)
    if x > y:
        n = math.ceil(x / y) * x + y
    else:
        n = (x + y) // 2
    print(n)
