Jack feels good with Rose, as Rose is a master of math. However, Rose sets a higher standard on Jack, to improve Jack's ability of math. So today Rose as usual sets a math question to Jack.
Given an integer and a sequence , , , , one position is if and only if there exists where , and the weight of this sequence is defined as the number of Good positions in this sequence.
Given and , for every between and ( and included), calculate .
Note that is the set of sequences satisfying .
Each output should module .

The only line contains two integers ,  (, ).

Output  integers in one line, as the description above indicated.

3 3

22 5 0