Semi-equations
Practice
4.2 (5 votes)
Linear algebra
Algorithms
Matrix exponentiation
Math
Problem
15% Success 2061 Attempts 30 Points 2s Time Limit 256MB Memory 1024 KB Max Code

You are given $$t$$ test cases. Each test case contains an integer $$n$$. Find the value of the following function:

 

such that 

  • \(f[0] = 0, f[1]=1, f[2]=1 ,....,f[n]=f[n-1]+f[n-2]. \)

Formally, you are required to find the summation from $$i=0$$ to $$i=n$$ for $${f[i]}$$.

Input format

  • The first line contains an integer $$t$$ denoting the number of test cases.
  • Each of the next $$t$$ lines contains an integer $$n$$.

Output format

Print the answer as described above modulo $$10^9+7$$.

Constraints

$$1 \le   t  \le  10^5$$

$$1 \le  n  \le {10^{18}}$$

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Points:30
39 votes
Tags:
Linear AlgebraApprovedEasy-MediumReadyMathematicsMatrix Exponentiation