FIBPOL - Fibonacci Polynomial


Let F(n) be the nth member of the Fibonacci sequence:

F(0) = 0, F(1) = 1,  
F(n) = F(n-1)+F(n-2) (n > 1)

Consider the following Fibonacci polynomial:

A(x) = x F(1) + x2 F(2) + x3 F(3) + ... + xn F(n) + ....
= sigma(n = 0 to infinity) xn F(n)

Amazingly,

A(1/2) = 1/2 + 1/22 + 2/23 + 3/24 + .... + F(n)/2n + ... = 2

In this problem, we only considering the non-negative-integer value of A(x). Here are some examples of A(x) for specific x.

xA(x)
0 0
sqrt(2)-1 1
1/2 2
[sqrt(13)-2]/3 3
[sqrt(89)-5]/8 4

Find out if x is rational with the given value of A(x)

Input

The first line contains T, the number of test cases. The next T lines contains the value of A(x).

  • 0 <= Ax <= 10^17
  • 1 <= T <= 100000

Output

  • 1 if the given Ax yeilds a rational x, 0 otherwise

Example

Input:
5
0
1
2
3
4
Output:
1
0
1
0
0

hide comments
akhand_mishra: 2019-12-05 10:14:38

credits to project Euler

hacking_bot: 2018-03-20 14:10:19

For Those in doubt refer Project Euler problem 137
ans THIS --> https://oeis.org/A081018

anirudnits: 2017-10-31 09:36:16

is Ax always an integer?

bolderic: 2017-08-23 03:34:28

Have to say I got a feeling back to my senior high school doing some hard sequence problem

holmesherlock: 2017-04-01 21:45:31

excellent prob,,figured out the solution very early but getting it accepted costed me more than 20 WA..

Aditya Paliwal: 2017-02-01 16:25:30

Last edit: 2017-02-01 17:26:01
spartax: 2016-12-01 17:35:01

for c/cpp users, use long double

rahulpadhy: 2016-08-17 08:02:48

Hey Piyush.. This is my submission id : http://www.spoj.com/submit/FIBPOL/id=17521569
Can you please tell as to where I am going wrong ?

Re: You have WA for some large cases. Approach is correct.

Last edit: 2016-08-17 13:55:35
Min_25: 2016-06-10 16:13:46

Almost the same as Project Euler 137.
It should be mentioned in the description or in the Resource.

Last edit: 2016-06-10 16:27:19
Piyush Kumar: 2016-06-10 15:18:09

Test cases have been updated. Sorry for the inconvenience!


Added by:Piyush Kumar
Date:2015-09-04
Time limit:1s-3s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ASM64 GOSU JS-MONKEY SCM qobi
Resource:Project Euler