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 Python (3.8.2) (judge verdict: Accepted)

N, K = map(int, input().split())
gcd_list = [0] * K#K, K-1, K-2の順
MOD = 10 ** 9 + 7

for i in range(K, 0, -1):
  #print(i)
  ans2 = pow((K // i), N, MOD)#
  x = i
  while x <= K:
    ans2 -= gcd_list[K - x]
    x += i
  gcd_list[K - i] = ans2 % MOD
  
ans = 0  
for i in range(K):
  ans += (gcd_list[i] * (K - i)) % MOD
  
print(ans % MOD)