## 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 πn. For example, for π=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 πk-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 π‘t (1β€π‘β€1041β€tβ€104)Β β the number of test cases.

The first and only line of each test case contains two integers πn and πk (2β€πβ€1092β€nβ€109; 1β€πβ€1091β€kβ€109).

### Special Numbers solution codeforces

For each test case, print one integerΒ β the πk-th special number in increasing order modulo 109+7109+7.

### Special Numbers solution codeforces

Example

3 3 4 2 12 105 564

### Special Numbers solution codeforces

output

9 12 3595374

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