Hi all my euler 29 is off by 200 where I get 9048 rather than the 9183

I attempted to find the ans search for it in the list (I used a binary search since linear was taking very long) and would just recieve the value 9048 somehow, I don’t know if there is something wrong with the searching aspect and many distinct powers are getting discarded as repeats by code by accident.

Here is my code

def insertionSort(list):
  for i in range(1, len(list)):
    key = list[i]
    j = i-1
    while j >= 0 and key < list[j] :
      list[j + 1] = list[j]
      j -= 1
    list[j+1] = key

def binary_search(list, ans):
  insertionSort(list)
  left = 0
  right = len(list) - 1
  while left <= right:
    mid = (left + right) // 2
    if list[mid] == ans:
      return mid
    elif list[mid] < ans:
      left = mid + 1
    else:
      right = mid - 1
  return -1

list=[]
for a in range(2,100):
  for b in range(2,100):
    yes=0
    ans=a**b
    result = binary_search(list,ans)
    if result==-1:
      list.append(ans)
print(len(list))

Looking for any help, thanks.