how to calculate 2^n modulo 1000000007 , n = 10^9

Question

what is the fastest method to calculate this, i saw some people using matrices and when i searched on the internet, they talked about eigen values and eigen vectors (no idea

Answer 1

Modular exponentiation by the square-and-multiply method:

function powerMod(b, e, m)
    x := 1
    while e > 0
        if e%2 == 1
            x, e := (x*b)%m, e-1
        else b, e := (b*b)%m, e//2
    return x