Suppose Bobo is at point $t_0$ on the time axis (number line), and he wants to use a time machine to return to the interval $(0, h]$.

When Bobo is at point $t$ on the time axis and the time machine has $c$ units of fuel, he can choose a non-negative integer $x$ such that $\lceil \frac{x}{h}\rceil \cdot h \leq c$. The time machine will then choose a random integer $y$ in $[0, x]$, causing Bobo to return to point $(t - y)$ while consuming $y$ units of fuel. (Here, $\lceil \cdot \rceil$ denotes the ceiling function.)

Due to the randomness of the time machine, given the parameters $h$ and the remaining fuel $c$, Bobo wants to know the maximum value of $t_0$ such that he is guaranteed to return to the interval $(0, h]$.

Input

The input contains multiple test cases. Process until the end of the file.

Each test case contains two integers $h$ and $c$.

Output

For each test case, output one integer representing the maximum value of $t_0$.

Examples

Input 1

100 99
100 100
100 149

Output 1

100
101
150

Note

For the first sample case, since the remaining fuel $c = 99 < 100$, Bobo can only choose $x = 0$, which results in $y = 0$. Therefore, if $t_0 > h = 100$, Bobo will definitely not be able to return to the target interval.

For the second sample case, when $t_0 = 102$, choosing $x = 2$ might result in $y = 1$, placing him at $t = 99$ with $c = 99$ fuel, which means the task fails. Thus, $t_0 < 102$.

Constraints

• $1 \leq h \leq 10^9$
• $0 \leq c \leq 10^9$
• The number of test cases does not exceed $10^5$.