Dicy Sequence

###Problem Statement: You are challenged to a dice game , however the dice you are given is rigged. There are 6 digits on the dice `1,2,3,4,5,6` and the maximum times they can be consecutively rolled is `A(1),A(2),A(3),A(4),A(5),A(6)` respectively. You can roll the dice `N` times and you have to tell the number of unique sequences that can be possibly obtained. Print the answer modulo `10^9