Description
In number theory, an abundant number is a natural number whose sum of all positive divisors, excluding itself, is greater than the number itself. For example, the sum of the proper divisors of 20 is 1+2+4+5+10=22 > 20, which is greater than the original number 20, so 20 is an abundant number. Write a program that takes two positive integers as input and outputs the number of abundant numbers between them.
Input
The number of test cases (t) is entered on the first line. (1 <= t <= 10)
Starting from the next line, t lines of two positive integers (m,n) are entered, one pair per line. (1 <= m <= n <= 100,000)
Output
For each test case, print the two input integers m and n connected by a hyphen (-), followed by a colon (:) and the number of abundant numbers on a separate line.
If no abundant numbers exist, print 'NO'. (Refer to sample output format.)