N-th Fibonacci Number Problem Statement

Given an integer ‘N’, your task is to find and return the N’th Fibonacci number using matrix exponentiation.

Since the answer can be very large, return the answer modulo 10^9 + 7.

Formula:

F(n) = F(n-1) + F(n-2), 
Where, F(1) = F(2) = 1.

Example:

Input:

N = 5

Output:

5

Input:

The first line contains a single integer ‘T’ denoting the number of test cases to be run. Then the test cases follow. The first line of each test case contains a single integer ‘N’, representing the integer for which we have to find its equivalent Fibonacci number. 

Output:

For each test case, print a single integer representing the N’th Fibonacci number. Return the answer modulo 10^9 + 7. Output for each test case will be printed in a separate line. 

Constraints:

• 1 <= T <= 10
• 1 <= N <= 10^5
• Time Limit: 1 sec.

Note:

You are not required to print anything; it has already been taken care of. Just implement the function. 

Follow Up:

Can you solve it in Time Complexity better than O(N)?