1160 Forever

Statement

Metadata

作者: 陈越
单位: 浙江大学
代码长度限制: 16 KB
时间限制: 3000 ms
内存限制: 64 MB

"Forever number" is a positive integer $A$ with $K$ digits, satisfying the following constrains:

the sum of all the digits of $A$ is $m$ ;
the sum of all the digits of $A+1$ is $n$ ; and
the greatest common divisor of $m$ and $n$ is a prime number which is greater than 2.

Now you are supposed to find these forever numbers.

Input Specification

Each input file contains one test case. For each test case, the first line contains a positive integer $N$ ( $\le 5$ ). Then $N$ lines follow, each gives a pair of $K$ ( $3$ ) and $m$ ( $1$ ), of which the meanings are given in the problem description.

Output Specification

For each pair of $K$ and $m$ , first print in a line Case X, where X is the case index (starts from 1). Then print $n$ and $A$ in the following line. The numbers must be separated by a space. If the solution is not unique, output in the ascending order of $n$ . If still not unique, output in the ascending order of $A$ . If there is no solution, output No Solution.

Sample Input

2
6 45
7 80

Sample Output

Case 1
10 189999
10 279999
10 369999
10 459999
10 549999
10 639999
10 729999
10 819999
10 909999
Case 2
No Solution

Last update: May 4, 2022