Circular Numbers

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Points: 10

Time limit: 1.0s

Memory limit: 16M

Problem type

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

Input Specification

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

Output Specification

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

Sample Input

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1
53 4

Sample Output

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132832080200501253

Comments

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d commented on Aug. 9, 2022, 7:07 a.m. ← edit 2 →
$10 \le XY \le 99$ $10 \leq X Y \leq 99$ and $2 \le D \le 9$ $2 \leq D \leq 9$

The circular number can have leading zeroes.

If you test beyond $255$ $255$ digits, you will get WA. In some test cases, the smallest answer exceeds $255$ $255$ digits.