Vasya decided to go to the grocery store. He found in his wallet $$$a$$$ coins of $$$1$$$ burle and $$$b$$$ coins of $$$2$$$ burles. He does not yet know the total cost of all goods, so help him find out $$$s$$$ ($$$s \gt 0$$$): the minimum positive integer amount of money he cannot pay without change or pay at all using only his coins.

For example, if $$$a=1$$$ and $$$b=1$$$ (he has one $$$1$$$-burle coin and one $$$2$$$-burle coin), then:

he can pay $$$1$$$ burle without change, paying with one $$$1$$$-burle coin,
he can pay $$$2$$$ burle without change, paying with one $$$2$$$-burle coin,
he can pay $$$3$$$ burle without change by paying with one $$$1$$$-burle coin and one $$$2$$$-burle coin,
he cannot pay $$$4$$$ burle without change (moreover, he cannot pay this amount at all).

So for $$$a=1$$$ and $$$b=1$$$ the answer is $$$s=4$$$.

Input

The first line of the input contains an integer $$$t$$$ ($$$1 \le t \le 10^4$$$) — the number of test cases in the test.

The description of each test case consists of one line containing two integers $$$a_i$$$ and $$$b_i$$$ ($$$0 \le a_i, b_i \le 10^8$$$) — the number of $$$1$$$-burle coins and $$$2$$$-burles coins Vasya has respectively.

Output

For each test case, on a separate line print one integer $$$s$$$ ($$$s \gt 0$$$): the minimum positive integer amount of money that Vasya cannot pay without change or pay at all.

Note

The first test case of the example is clarified into the main part of the statement.
In the second test case, Vasya has only $$$1$$$ burle coins, and he can collect either any amount from $$$1$$$ to $$$4$$$, but $$$5$$$ can't.
In the second test case, Vasya has only $$$2$$$ burle coins, and he cannot pay $$$1$$$ burle without change.
In the fourth test case you don't have any coins, and he can't even pay $$$1$$$ burle.

Vasya and Coins

Examples