Longest Good Array
Description
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 $r$.
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 $r$ ($1\le l\le r\le 10^9$).
For each test case, output a single integer — the length of the longest good array Sakurako can form given $l$ and $r$.
Input
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
For each test case, output a single integer — the length of the longest good array Sakurako can form given $l$ and $r$.
5
1 2
1 5
2 2
10 20
1 1000000000
2
3
1
5
44721
Note
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 $(10,11,13,16,20)$.