## Circular Numbers

An (XY, D)—CIRCULAR NUMBER is a number whose last two digits are X and Y, and multiplication of the number by the single digit D is equivalent to moving the last two digits (XY) to the beginning of the number. For example, the number 132832080200501253 is a (53, 4)—CIRCULAR NUMBER because 132832080200501253 * 4 = 531328320802005012. Write a program that asks for two-digit number XY and a single digit D, and prints the SMALLEST (XY, D)—CIRCULAR NUMBER or prints a message NONE if none exists. It is guaranteed that your number will not exceed 255 digits.

### INPUT

An integer number, N, indicating the total number of cases. On each of the next N lines are the two-digit number XY and the single digit D, separated by a space.### OUTPUT

The smallest circular number (if one exists with less than 255 digits) that satisfies the given condition; otherwise output the message NONE.### SAMPLE DATA

Input file

1 53 4

Output file

132832080200501253

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Best Solutions

**Point Value:** 10

**Time Limit:** 2.00s

**Memory Limit:** 16M

**Added:** Feb 24, 2009

**Languages Allowed:**

C++03, PAS, C, HASK, ASM, RUBY, PYTH2, JAVA, PHP, SCM, CAML, PERL, C#, C++11, PYTH3

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