#EXLAGFIB. Extremely Lagged Fibonacci
Extremely Lagged Fibonacci
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Let $(\ a_i\ )_{i=0}^\infty$ be the integer sequence such that: $$a_n = \begin{cases} 0 & (0 \le n < k - 1) \\ 1 & (n = k - 1)\\ b \cdot a_{n-j} + c \cdot a_{n-k} & (n \ge k) \end{cases}, $$ where $j$, $k$, $b$ and $c$ is integer.
For each $n, j, k, b$ and $c$, find $a_n$ modulo $1\,000\,000\,037$.
Input
The first line contains $T$, the number of test cases.
Each of the next $T$ lines contains five integers $n, j, k, b$ and $c$.
Output
For each test case, print $a_n$ modulo $1\,000\,000\,037$.
Constraints
- $1 \le T \le 10^2$
- $0 \le n \le 10^9$
- $10^5 \le k \le 10^8$, $1 \le j < k$
- $1 \le b \le 10^9$, $1 \le c \le 10^9$
Example
Input: 2 1000000 1 100000 1 1 1000000000 1 100000000 1 1</p>Output: 372786243 994974348