C. Longest Good Array
binary search; brute force; math
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 \(r\).
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 \((10,11,13,16,20)\).