Hip To Be Square

Time Limit: 5 Seconds    Memory Limit: 65536 KB

None of the numbers 6, 10, 15 is a square, but their product, the number 900, is a square. We are interested in sets of positive integers, the product of which is a square. We call such a set HIP (this stands for Has Interesting Product). Evidently {6, 10, 15} is HIP, and so is {25}. 

More generally, given a set of positive integers, does it have a non-empty subset which is HIP, and if so, for which of the HIP subsets will the product be minimal? 

To make things slightly easier for you, we restrict our attention to intervals.

 

Input

Each test case consists of two integers a and b on a single line (1 < a < b ≤ 4900). These integers describe the interval A = { x ∈ N | a ≤ x ≤ b }.

 

Output

For each test case, print the least number k such that the product of the elements of some non-empty subset X ⊆ A equals k² . If no such number exists, print ‘none’. The number k will be less than 2⁶³ .

 

Sample Input

20 30 
101 110 
2337 2392 

Sample Output

5
none
3580746020392020480

Submit

Source: NWERC 2012