Nezuko suddenly woke up on the number line at point $$$0$$$ and has $$$h$$$ health points. She wants to reach point $$$d$$$. In one turn, she can do exactly one of two things:

rest in the shade and increase her current health by $$$1$$$;
move from her current position $$$x$$$ to $$$x + 1$$$.

Each movement decreases Nezuko's health; if the movement is the $$$j$$$-th consecutive movement, her health will decrease by $$$j$$$ points. If as a result of a move Nezuko's health drops to $$$0$$$ or below, she cannot make that move.

For example, if Nezuko initially had $$$7$$$ health points and $$$d=4$$$, her moves could look like this:

Move from $$$0$$$ to $$$1$$$ and decrease health by $$$1$$$. Now she is at point $$$1$$$ with $$$6$$$ health points.
Move from $$$1$$$ to $$$2$$$ and decrease health by $$$2$$$. Now she is at point $$$2$$$ with $$$4$$$ health points.
Move from $$$2$$$ to $$$3$$$ and decrease health by $$$3$$$. Now she is at point $$$3$$$ with $$$1$$$ health point.
Rest and restore $$$1$$$ health point. Now she is at point $$$3$$$ with $$$2$$$ health points.
Move from $$$3$$$ to $$$4$$$ and decrease health by $$$1$$$. Now she is at point $$$4$$$ with $$$1$$$ health point.

Find the minimum number of turns required for her to reach point $$$d$$$.

Input

Each test consists of several test cases.

The first line contains one integer $$$t$$$ ($$$1 \le t \le 10^4$$$) — the number of test cases. The following describes the test cases.

The first line of each test case contains two integers $$$h$$$ and $$$d$$$ $$$(1\le h,d \le 10^9)$$$ — the number of health points and the destination point, respectively.

Output

For each test case, output one number — the minimum number of turns required for Nezuko to reach point $$$d$$$.

Note

In the first test case, $$$h = 3$$$, $$$d = 2$$$ the actions could be as follows:

Move from $$$0$$$ to $$$1$$$ and decrease health by $$$1$$$. Now she is at point $$$1$$$ with $$$2$$$ health points.
Rest and restore $$$1$$$ health point. Now she is at point $$$1$$$ with $$$3$$$ health points.
Move from $$$1$$$ to $$$2$$$ and decrease health by $$$1$$$. Now she is at point $$$2$$$ with $$$2$$$ health points.

In total, $$$3$$$ turns.

In the fourth test case, $$$h = 2$$$, $$$d = 4$$$ the actions could be as follows:

Move from $$$0$$$ to $$$1$$$ and decrease health by $$$1$$$. Now she is at point $$$1$$$ with $$$1$$$ health point.
Rest and restore $$$1$$$ health point. Now she is at point $$$1$$$ with $$$2$$$ health points.
Move from $$$1$$$ to $$$2$$$ and decrease health by $$$1$$$. Now she is at point $$$2$$$ with $$$1$$$ health point.
Rest and restore $$$1$$$ health point. Now she is at point $$$2$$$ with $$$2$$$ health points.
Move from $$$2$$$ to $$$3$$$ and decrease health by $$$1$$$. Now she is at point $$$3$$$ with $$$1$$$ health point.
Rest and restore $$$1$$$ health point. Now she is at point $$$3$$$ with $$$2$$$ health points.
Move from $$$3$$$ to $$$4$$$ and decrease health by $$$1$$$. Now she is at point $$$4$$$ with $$$1$$$ health point.

In total, $$$7$$$ turns.

Idx	Name	Rating
A	Be Positive	800
B	Unconventional Pairs	800
C	MEX rose	900
D	A and B	1200
E	Hidden Knowledge of the Ancients	1500
F	Nezuko in the Clearing	1900
G	Buratsuta 3	2100

Codeforces Round 1054 (Div. 3)