Special Numbers

题意翻译

如果一个正整数可以被表示为 $n$ 的若干个**不同的**非负整数次幂的和，则称这个正整数是**特别**的。 例如，当 $n = 4$ 时，$17$ 是特别的，因为它可以表示为 $4^0 + 4^4 = 1 + 16 = 17$，而 $9$ 不是特别的。 每个测试点包含 $t$ 组数据，每组数据给定两个正整数 $n$ 和 $k$，请求出第 $k$ 小的特别的数。 其中 $1 \le t \le 10^4$，$2 \le n \le 10^9，1 \le k \le 10^9$。 答案可能很大，请输出答案对 $10^9 + 7$ 取模的结果。

题目描述

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 $ .

输入输出格式

输入格式

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 $ ).

输出格式

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

输入输出样例

输入样例 #1

3
3 4
2 12
105 564

输出样例 #1

9
12
3595374

说明

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