[Solution] Special Numbers solution codeforces

Special Numbers solution codeforces


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 𝑛n. For example, for 𝑛=4n=4 number 1717is special, because it can be written as 40+42=1+16=1740+42=1+16=17, but 99 is not.

Theofanis asks you to help him find the π‘˜k-th special number if they are sorted in increasing order. Since this number may be too large, output it modulo 109+7109+7.

Special Numbers solution codeforces

Input

The first line contains a single integer 𝑑t (1≀𝑑≀1041≀t≀104)Β β€” the number of test cases.

The first and only line of each test case contains two integers 𝑛n and π‘˜k (2≀𝑛≀1092≀n≀109; 1β‰€π‘˜β‰€1091≀k≀109).

Special Numbers solution codeforces

Output

For each test case, print one integerΒ β€” the π‘˜k-th special number in increasing order modulo 109+7109+7.

Special Numbers solution codeforces

Example

input

Copy
3
3 4
2 12
105 564

Special Numbers solution codeforces

output

Copy
9
12
3595374
Note

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

 

Special Numbers solution codeforces


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