EXLAGFIB - Extremely Lagged Fibonacci


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

Output:
372786243
994974348

hide comments
Min_25: 2016-09-22 13:27:38

@:D
Thank you ! My best (total) time is around 0.24 sec.

:D: 2016-09-22 02:16:20

Great problem. Seems like another variant on fib / recursive sequences, but it's actually really original. Finding efficient solution was very interesting. Thanks for setting it up min_25!

P.S. For reference, what's your best time on this problem?

Last edit: 2016-09-22 02:17:17
Min_25: 2016-04-26 19:29:46

@Blue.Mary
Thanks, 1KB limit was tough for me ... :)

Last edit: 2016-04-26 19:29:55
[Rampage] Blue.Mary: 2016-04-25 06:25:31

A 1024 byte source limit may make this problem more interesting :-)


Added by:Min_25
Date:2016-04-25
Time limit:5s-8s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ASM64 GOSU JS-MONKEY