CF1594B Special Numbers

Theofanis really likes sequences of positive integers, thus his teacher (Yeltsa Kcir) gave him a problem about a sequence that consists of only special numbers. Let's call a positive number special if it can be written as a sum of different non-negative powers of $ n $ . For example, for $ n = 4 $ number $ 17 $ is special, because it can be written as $ 4^0 + 4^2 = 1 + 16 = 17 $ , but $ 9 $ is not. Theofanis asks you to help him find the $ k $ -th special number if they are sorted in increasing order. Since this number may be too large, output it modulo $ 10^9+7 $ .

The first line contains a single integer $ t $ ( $ 1 \le t \le 10^4 $ ) — the number of test cases. The first and only line of each test case contains two integers $ n $ and $ k $ ( $ 2 \le n \le 10^9 $ ; $ 1 \le k \le 10^9 $ ).

For each test case, print one integer — the $ k $ -th special number in increasing order modulo $ 10^9+7 $ .

For $ n = 3 $ the sequence is $ [1,3,4,9...] $