output_description: Print the sum of \gcd(A_1, ..., A_N) over all K^N sequences, modulo (10^9+7).
  
  * * *
input_description: Input is given from Standard Input in the following format:
  
      
      
      N K
attempt: N, K = [int(n) for n in input().split()]
  NUM = 1000000007
  
  
  def modpow(a, b):  # (a ** b) % NUM
      ans = 1
      while b != 0:
          if b % 2 == 1:
              ans *= a
              ans %= NUM
          a = a * a
          a %= NUM
          b //= 2
      return ans
  
  
  C = [0 for _ in range(K + 1)]
  for d in range(K):
      k = K - d  # K ... 1
      L = K // k
      C[k] = modpow(L, N)  # A = 1*k ... L*k
      for l in range(2, L + 1):
          C[k] -= C[l * k]
          if C[k] < 0:
              C[k] += NUM
          C[k] %= NUM
  
  ans = 0
  for k in range(1, K + 1):
      ans += k * C[k]
      ans %= NUM
  print(ans)
  
problem_description: 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.
samples: [{"input": "3 2", "output": "9\n    \n\n\\gcd(1,1,1)+\\gcd(1,1,2)+\\gcd(1,2,1)+\\gcd(1,2,2)\n+\\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\n\nThus, the answer is 9.\n\n* * *"}, {"input": "3 200", "output": "10813692\n    \n\n* * *"}, {"input": "100000 100000", "output": "742202979\n    \n\nBe sure to print the sum modulo (10^9+7)."}]