Circular Numbers

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Points: 10

Time limit: 1.0s

Memory limit: 16M

Problem type

An $(XY, D)$ ~(XY, 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 ( $XY$ ~XY~) to the beginning of the number. For example, the number $132832080200501253$ ~132832080200501253~ is a $(53, 4)$ ~(53, 4)~-CIRCULAR NUMBER because $132832080200501253 \times 4 = 531328320802005012$ . Write a program that asks for a two-digit number $XY$ ~XY~ and a single digit $D$ ~D~, and prints the smallest $(XY, D)$ ~(XY, 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 $XY$ ~XY~ 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

1
53 4

Sample Output

132832080200501253

Comments

0
d commented on Aug. 9, 2022, 7:07 a.m. ← edit 2 →
$10 \le XY \le 99$ ~10 \le XY \le 99~ and $2 \le D \le 9$ ~2 \le D \le 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.