You have two positive integers $a$ and $b$.

You can perform two kinds of operations:

• $a = \lfloor \frac{a}{b} \rfloor$ (replace $a$ with the integer part of the division between $a$ and $b$)
• $b=b+1$ (increase $b$ by $1$)

Find the minimum number of operations required to make $a=0$.

Input

The first line contains a single integer $t$ ($1 \le t \le 100$) — the number of test cases.

The only line of the description of each test case contains two integers $a$, $b$ ($1 \le a,b \le 10^9$).

Output

For each test case, print a single integer: the minimum number of operations required to make $a=0$.

Note

In the first test case, one of the optimal solutions is:

1. Divide $a$ by $b$. After this operation $a = 4$ and $b = 2$.
2. Divide $a$ by $b$. After this operation $a = 2$ and $b = 2$.
3. Increase $b$. After this operation $a = 2$ and $b = 3$.
4. Divide $a$ by $b$. After this operation $a = 0$ and $b = 3$.

Samples

6
9 2
1337 1
1 1
50000000 4
991026972 997
1234 5678

4
9
2
12
3
1