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 $10^9+7$.

西奥法尼斯非常喜欢正整数序列，因此他的老师（耶尔察·克希尔）给他出了一道关于仅由特殊数字构成的序列的问题。

我们称一个正整数为特殊数，当且仅当它可以表示为若干个互不相同的、以 $n$ 为底的非负整数次幂之和。例如，当 $n = 4$ 时，数 $17$ 是特殊数，因为它可以写成 $4^0 + 4^2 = 1 + 16 = 17$；但 $9$ 不是特殊数。

西奥法尼斯请你帮助他找出从小到大排序后的第 $k$ 个特殊数。由于该数可能非常大，请输出它对 $10^9+7$ 取模的结果。

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 $k$ ($2 \le n \le 10^9$; $1 \le k \le 10^9$).

第一行包含一个整数 $t$（$1 \le t \le 10^4$）—— 表示测试用例的数量。

每个测试用例仅有一行，包含两个整数 $n$ 和 $k$（$2 \le n \le 10^9$；$1 \le k \le 10^9$）。

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

对于每个测试用例，输出一个整数——第 $k$ 个特殊数（按升序排列）对 $10^9+7$ 取模的结果。

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

当 $n = 3$ 时，该序列为 $[1,3,4,9\ldots]$