Linear recursive sequence

A well-known linear recursive sequence f(n) is defined as follows.

For k≤0, f(k)=1
For k≥1, f(k)=a*f(k - p)+b*f(k - q).

Given n,a,b,p,q, find the value of f(n) modulo 119.

The input consists of several tests. For each tests:

5 integers n,a,b,p,q (1≤n≤10⁹,0≤a,b≤10⁹,1≤p<q≤10⁴).

For each tests:

A single integer f(n).

1 1 1 1 2
1000000000 1 2 3 4

2
[b]100[/b]

Xiaoxu Guo (ftiasch)

2014 Multi-University Training Contest 5