You are a product manager and currently leading a team to develop a new product. Unfortunately, the latest version of your product fails the quality check. Since each version is developed based on the previous version, all the versions after a bad version are also bad.

Suppose you have n versions [1, 2, ..., n] and you want to find out the first bad one, which causes all the following ones to be bad.

You are given an API bool isBadVersion(version) which returns whether version is bad. Implement a function to find the first bad version. You should minimize the number of calls to the API.

Example 1:
Input: n = 5, bad = 4
Output: 4
Explanation:
call isBadVersion(3) -> false
call isBadVersion(5) -> true
call isBadVersion(4) -> true
Then 4 is the first bad version.

Example 2:
Input: n = 1, bad = 1
Output: 1\

Constraints: 1 <= bad <= n <= 231 - 1

Intuitively, we know that the product versions is a sequence of good versions, followed by a group of bad versions. This means that we are looking for the first index which isBadVersion(ans) returns true. Therefore, we must update the answer when we find a smaller version that is bad, repeat until we find the smallest.

def firstBadVersion(self, n: int) -> int:
    left, right = 1, n
    ans = -1

    while left <= right:
        mid = (left + right) // 2
        if isBadVersion(mid):
            ans = mid
            right = mid - 1
        else:
            left = mid + 1

    return ans