The Little Detective and the Kid are tired of fighting with each other, so they try to find the winner by a simple problem.

Kid gives the Detective an array A of size N and challenges him to find the following sum :

Where
Fib (i) is the famous Fibonacci sequence such that Fib (0) =0 , Fib(1) = 1 and Fib(i) = Fib(i-1) + Fib(i-2) for i>=2.
GCD (x,y) represents the greatest common divisor of x and y.
Since the answer can be very large, Kid asks Little Detective to find it modulo 1000000007. Help Detective find the answer and tell Kid who is the real artist.

Input :

First line of input contains two space separated integers N and K.
Second line of input contains N space separated integers A_i.

Output :

Single integer denoting the value of S modulo 1000000007.

Constraints :

0 < N <= 100000
0 < K <= 10¹⁵
0 < A_i <= 1000000

Example

Input:

5 1
2 4 2 1 4

Output:

12