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## ACM_0106 - QUITE GOOD NUMBERS

A "perfect" number is an integer that is equal to the sum of its divisors (where 1 is considered a divisor).  For example, 6 is perfect because its divisors are 1, 2, and 3, and 1 + 2 + 3 is 6. Similarly, 28 is perfect because it equals 1 + 2 + 4 + 7 + 14.

A "quite good" number is an integer whose "badness" – the absolute value of the difference between the sum of its divisors and the number itself – is not greater than a specified value. For example, if the allowable badness is set at 2, there are 11 "quite good" numbers less than 100: 2, 3, 4, 6, 8, 10, 16, 20, 28, 32, and 64. But if the allowable badness is set at 0 (corresponding to the "perfect" numbers) there are only 2: 6 and 28.

Your task is to write a program to count how many quite good numbers (of a specified maximum badness) fall in a specified range.

#### Input

Input will consist of specifications for a series of tests.  Information for each test is a single line containing 3 integers with a single space between items:

• start (2 <= start < 1000000) specifies the first number to test
• stop (start <= stop < 1000000) specifies the last number to test
• badness (0 <= badness < 1000) specifies the maximum allowable badness A line containing 3 zeros terminates the input.

#### Output

Output should consist of one line for each test comprising the test number (formatted as shown) followed by a single space and the number of values in the test range with badness not greater than the allowable value.

#### Examples

 № stdin stdout 1 2 100 2 2 100 0 1000 9999 3 0 0 0 Test 1: 11 Test 2: 2 Test 3: 6

 Ավելացրեց. Հրանտ Հովհաննիսյան (ԳՏՏԿ) Ամսաթիվ. 2014-01-29 Ժամանակի սահմանափակումը. 1s Ծրագրի տեքստի սահմանափակումը. 50000B Memory limit: 1536MB Cluster: Cube (Intel G860) Լեզուներ. Բոլորը բացի ASM32 ASM64 GAWK CLPS CLOJURE D ERL FSHARP FORTRAN GOSU HASK ICON ICK NEM NIM OBJC-CLANG PICO PIKE PYPY PY_NBC RUST SCM guile CHICKEN SED TCL WHITESPACE Աղբյուրը. Australian Programming Contest 2013.A