PROBLEM LINK:
Author:Suraj Kumar
Tester:Priyanshu Jain
DIFFICULTY:
EASY
PREREQUISITES:
Matrix form of Fibonacci numbers, Binary exponentiation.
PROBLEM:
You just need to find the nth Fibonacci number modulo 10^9+7.
EXPLANATION:
It is a 2x2 matrix A with A[0][0]=1, A[0][1]=1, A[1][0]=1, A[1][1]=0. With this matrix form one can calculate the nth
Fibonacci just by raising the matrix to the power n. A[0][1] will give you the nth Fibonacci number.
How to find the answer modulo 10^9+7.
Use the Binary Exponentiation technique. If the number becomes greater than 10^9+7 after the multiplication
then the elements of the matrix is replaced by their modulo 10^9+7.
Click here for more details.
AUTHOR'S AND TESTER'S SOLUTIONS:
Author's solution can be found here.