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May 23rd, 2019
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  1. num = input()
  2. k = int(input())
  3.  
  4. div3 = int(num) % 3 == 0
  5.  
  6. a2 = 0
  7. a5 = 0
  8.  
  9. for c in num:
  10. if c in '2468':
  11. a2 += 1
  12. if c == '5':
  13. a5 += 1
  14.  
  15. pairs = (len(num)*(len(num) - 1)) / 2
  16. ax = len(num) - a2 - a5
  17.  
  18. data = list()
  19.  
  20. data.append([0, 0, 0])
  21.  
  22. if num[-1] in '2468':
  23. data[0][1] = 1
  24. elif num[-1] == '5':
  25. data[0][2] = 1
  26. else:
  27. data[0][0] = 1
  28.  
  29. for i in range(k):
  30.  
  31. data.append([data[i][0] * (1 - (a2 + a5)/pairs) + data[i][1] * (ax/pairs) + data[i][2] * (ax/pairs),
  32. data[i][0] * (a2/pairs) + data[i][1] * (1 - (ax + a5)/ pairs) + data[i][2] * (a2 / pairs),
  33. data[i][0] * (a5 / pairs) + data[i][1] * (a5 / pairs) + data[i][2] * (1 - (ax + a2)/ pairs)])
  34.  
  35. answer = data[k][2]
  36.  
  37. if (div3):
  38. answer += data[k][1]
  39.  
  40. print(answer)
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