output_description: Print the sum of the answers to the questions for the integers between 0 and X
  (inclusive), modulo 998244353.
  
  * * *
input_description: Input is given from Standard Input in the following format:
  
      
      
      N
      X
attempt: N = int(input())
  X = int(input(), 2)
  MOD = 998244353
  ans = ((X + 1) % MOD) * 2 * N
  L = []
  for i in range(1, N // 3 + 1):
      if N % (2 * i) == i:
          for j in range(2**i):
              b = int(
                  (("0" * i + bin(j)[2:])[-i:] + ("0" * i + bin(2**i - j - 1)[2:])[-i:])
                  * (N // (2 * i))
                  + ("0" * i + bin(j)[2:])[-i:],
                  2,
              )
              if X >= b and not (b in L):
                  L.append(b)
                  ans -= 2 * N
                  ans += 2 * i
                  ans %= MOD
  print(ans)
  
problem_description: Statement
  
  Given are integers N and X. For each integer k between 0 and X (inclusive),
  find the answer to the following question, then compute the sum of all those
  answers, modulo 998244353.
  
    * Let us repeat the following operation on the integer k. Operation: if the integer is currently odd, subtract 1 from it and divide it by 2; otherwise, divide it by 2 and add 2^{N-1} to it. How many operations need to be performed until k returns to its original value? (The answer is considered to be 0 if k never returns to its original value.)
samples: [{"input": "3\n    111", "output": "40\n    \n\nFor example, for k=3, the operation changes k as follows: 1,0,4,6,7,3.\nTherefore the answer for k=3 is 6.\n\n* * *"}, {"input": "6\n    110101", "output": "616\n    \n\n* * *"}, {"input": "30\n    001110011011011101010111011100", "output": "549320998"}]