A14606. 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 $[1,3,4,9...]$