Problem:
Score : 500 points

Problem Statement

Consider sequences \{A_1,...,A_N\} of length N consisting of integers between 1 and K (inclusive).

There are K^N such sequences. Find the sum of \gcd(A_1, ..., A_N) over all of them.

Since this sum can be enormous, print the value modulo (10^9+7).

Here \gcd(A_1, ..., A_N) denotes the greatest common divisor of A_1, ..., A_N.

Constraints

2 \leq N \leq 10^5

1 \leq K \leq 10^5

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N K

Output

Print the sum of \gcd(A_1, ..., A_N) over all K^N sequences, modulo (10^9+7).

Sample Input 1

3 2

Sample Output 1

9

\gcd(1,1,1)+\gcd(1,1,2)+\gcd(1,2,1)+\gcd(1,2,2)
+\gcd(2,1,1)+\gcd(2,1,2)+\gcd(2,2,1)+\gcd(2,2,2)
=1+1+1+1+1+1+1+2=9

Thus, the answer is 9.

Sample Input 2

3 200

Sample Output 2

10813692

Sample Input 3

100000 100000

Sample Output 3

742202979

Be sure to print the sum modulo (10^9+7).

Solution in Ruby (2.7.1) (judge verdict: Wrong Answer)

n,k=gets.split(' ').map(&:to_i)
#h=gets.split(' ').map(&:to_i)
#tajigen = Array.new(4) { Array.new(2,0) }
#maze = h.times.map { gets.chomp }
wari = Array.new(k+1)
for i in 1..k
  wari[i] = (k/i)**n
end
#puts wari
wari[0] = 0
for i in 0..(k/2-1)
  put = k/2-i
  count=2
  while put * count <= k
    wari[put]=wari[put] - wari[put * count]
    count+=1
  end
end

#puts wari
ans=0
for i in 1..k
  ans += i * wari[i]
end
puts ans