Special Numbers codeforces solution- 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 1717 is special, because it can be written as 40+42=1+16=1740+42=1+16=17, but 99 is not.

Special Numbers codeforces solution

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 1717 is 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 kk-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

The first line contains a single integer tt (1≤t≤1041≤t≤104) — the number of test cases.

The first and only line of each test case contains two integers nn and kk (2≤n≤1092≤n≤109; 1≤k≤1091≤k≤109).

Special Numbers solution codeforces

For each test case, print one integer — the kk-th special number in increasing order modulo 109+7109+7.

Example

input

Copy
3
3 4
2 12
105 564

Special Numbers solution codeforces

Copy
9
12
3595374
Note

For n=3n=3 the sequence is [1,3,4,9…]

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