Codeforces Round 747 (Div. 2) |
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Finished |

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bitmasks

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B. Special Numbers

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputTheofanis 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 $$$10^9+7$$$.

Input

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

Output

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

Example

Input

3 3 4 2 12 105 564

Output

9 12 3595374

Note

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

Codeforces (c) Copyright 2010-2023 Mike Mirzayanov

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