Problem B
Super Number
Input: Standard Input

Output: Standard Output

Time Limit: 3 Seconds

 

Don't you think 162456723 very special? Look at the picture below if you are unable to find its speciality. (a | b means b is divisible by a)

Figure: Super Numbers

 

Given n, m (0 < n < m < 30), you are to find a m-digit positive integer X such that for every i (n <= i <= m), the first i digits of X is a multiple of i. If more than one such X exists, you should output the lexicographically smallest one. Note that the first digit of X should not be 0.

 

Input 

The first line of the input contains a single integer t(1 <= t <= 15), the number of test cases followed. For each case, two integers n and m are separated by a single space.

 

Output 

For each test case, print the case number and X. If no such number, print -1.

 

Sample Input Output for Sample Input

2

1 10

3 29

Case 1: 1020005640

Case 2: -1

 


Problemsetter: Rujia Liu, Member of Elite Problemsetters' Panel

Special Thanks to:

Monirul Hasan (Alternate solution)

Shahriar Manzoor (Figure Drawing)