Social Distancing

You are given a string s and an integer k. Each character in the string is either '.' or 'x', where '.' represents an empty space and 'x' represents a person.

Return whether it’s possible to choose a position to stand on such that the distance between you and the closest person to you is at least k. (The distance between each neighbouring indices is 1).

Constraints

• 1 ≤ k ≤ n ≤ 100,000 where n is the length of s

https://binarysearch.com/problems/Social-Distancing

Examples

Example 1

Input

• s = x...x
• k = 2

Output

• answer = True

Explanation

You can stand at s[2].

Example 2

Input

• s = x..
• k = 2

Output

• answer = True

Explanation

You can stand at s[2]

Example 3

Input

• s = x..x
• k = 2

Output

• answer = False

Explanation

There’s a person standing next to both of the empty spaces (distance of 1).

Example 4

Input

• s = ..x
• k = 2

Output

• answer = True

Explanation

You can stand at s[0]

Example 5

Input

• s = .
• k = 1

Output

• answer = True

Explanation

You can stand at s[0]

Solution