CF2008C Longest Good Array

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) $ .