Bruce always comes up with new challenges for his students. On Saturday's class, Bruce gives Timothy two positive integers and , and asks Timothy to calculate the mod , where is the concatenation of all positive integers from to . For example, . Timothy is so smart that he immediately realizes that it is impossible to calculate the result by hand. Can you help Timothy to write a program to solve this question?
The input will consist of two integers, and , in one line.
In of the test cases, .
In of the test cases, and .
Output one integer, the result of .
Sample Input 1
Sample Output 1
Sample Input 2
Sample Output 2