Today, Sakurako was studying arrays. An array $$$a$$$ of length $$$n$$$ is considered good if and only if:

- the array $$$a$$$ is increasing, meaning $$$a_{i - 1} < a_i$$$ for all $$$2 \le i \le n$$$;
- the differences between adjacent elements are increasing, meaning $$$a_i - a_{i-1} < a_{i+1} - a_i$$$ for all $$$2 \le i < n$$$.

Sakurako has come up with boundaries $$$l$$$ and $$$r$$$ and wants to construct a good array of maximum length, where $$$l \le a_i \le r$$$ for all $$$a_i$$$.

Help Sakurako find the maximum length of a good array for the given $$$l$$$ and $$$r$$$.

Input format:
The first line contains a single integer $$$t$$$ ($$$1\le t\le 10^4$$$)  — the number of test cases.

The only line of each test case contains two integers $$$l$$$ and $$$r$$$ ($$$1\le l\le r\le 10^9$$$).
Output format:
For each test case, output a single integer  — the length of the longest good array Sakurako can form given $$$l$$$ and $$$r$$$.
Example Input 0:
5
1 2
1 5
2 2
10 20
1 1000000000

Example Output 0:
2
3
1
5
44721

Notes:
For $$$l=1$$$ and $$$r=5$$$, one possible array could be $$$(1,2,5)$$$. It can be proven that an array of length $$$4$$$ does not exist for the given $$$l$$$ and $$$r$$$.

For $$$l=2$$$ and $$$r=2$$$, the only possible array is $$$(2)$$$.

For $$$l=10$$$ and $$$r=20$$$, the only possible array is $$$(10,11,13,16,20)$$$.

Example input:
5
1 2
1 5
2 2
10 20
1 1000000000


Example output:
2
3
1
5
44721