Lower Bound

nums is sorted in non-decreasing order and may contain repeated values. Return the first index i with nums[i] >= target. If every value is smaller than target, return len(nums).

This is where target would be inserted to keep the list sorted, before any equal values.

Examples

Example 1

Input:

lower_bound([1, 2, 2, 2, 5], 2)

Output:

1

The first 2 is at index 1.

Example 2

Input:

lower_bound([1, 3, 5], 6)

Output:

3

Every value is smaller than 6, so the answer is the length, 3.

Constraints

• 0 <= len(nums) <= 2 * 10**5
• nums is sorted in non-decreasing order.
• -10**9 <= nums[i], target <= 10**9
• The big tests count how many values your code reads from the list (the limit is stated in the failure message). Reading every value, or using in, .index, .count, min or sorted on the whole list, fails them.