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- Project Euler #207: Integer partition equations

# Project Euler #207: Integer partition equations

# Project Euler #207: Integer partition equations

_{This problem is a programming version of Problem 207 from projecteuler.net}

For some positive integers , there exists an integer partition of the form ,

where , and are all positive integers and is a real number.

The first two such partitions are and .

Partitions where is also an integer are called .

For any let be the proportion of such partitions that are perfect with .

Thus .

In the following table are listed some values of

...

Find the smallest for which .

**Input Format**

First line of each test file contains a single integer that is the number of queries per test file. lines follow, with two integers and separated by a single space on each.

**Constraints**

**Output Format**

Print exactly lines with an answer for the corresponding query on each.

**Sample Input 0**

```
2
2 3
9 20
```

**Sample Output 0**

```
6
30
```

**Explanation 0**

, but , therefore, an answer for the first query is .

, which is the first value less than among all where .