For the cost of 5000 yen, Miyagi can ask Sendai to do whatever she wants! Today, Miyagi demands that Sendai make her an array... specifically, Miyagi only wants a very particular type of array. For arbitrary integers (b\geq 2) and (x\geq 1), define (v(b, x)) to be the maximal (k) satisfying (b^k \mid x); that is, the maximal (k) such that (x) is a multiple of (b^k). It can be shown that this is always a well-defined, nonnegative integer. You are given integers (n) and (m) satisfying (n\leq m). Find the maximum value of (\sum_{i=2}^n v(i, a_i)) across all arrays (a) of length (n) satisfying the following conditions: (a) is strictly increasing ; that is, for all (1\leq i\leq n-1), (a_i < a_{i+1}), and for all (1\leq i\leq n), (1\leq a_i\leq m). The first line contains a single integer (t) ((1 \leq t \leq 10^4)) — the number of test cases. The only line of each test case contains two integers (n) and (m) ((2\leq n\leq m \leq 2\cdot 10^5)). It is guaranteed that the sum of (m) over all test cases does not exceed (2\cdot 10^5). For each test case, output a single integer, the maximum value of (\sum_{i=2}^n v(i, a_i)) across all arrays (a) of length (n) satisfying the given conditions. In the first example, one possible array is (a = 6, 8, 9, 16) which yields a value of (3 + 2 + 2 = 7). It can be shown that this is the maximum value of (\sum_{i=2}^n v(i, a_i)) across all arrays (a) of length (n) satisfying the given conditions.