Maximize minimum value after k decrements

You are given an integer array vulnerabilities of length n, where vulnerabilities[i] is the initial security score of server i.

You must perform exactly k operations. In each operation, choose any server i and decrease vulnerabilities[i] by 1.

After all k operations, let the resulting array be final.

Task: Compute the maximum possible value of min(final) that you can achieve by choosing which servers to decrement each time.

Input

• Integer array vulnerabilities (length n )
• Integer k (number of operations)

Output

• An integer: the maximum achievable min(final)

Notes / Constraints (reasonable interview assumptions)

• 1 ≤ n ≤ 2e5
• 0 ≤ vulnerabilities[i] ≤ 1e9
• 0 ≤ k ≤ 1e12
• Decrements may make values negative.

Example

• vulnerabilities = [5, 1, 4] , k = 3
  • One optimal strategy is to decrement the 5 three times → [2, 1, 4] , so min = 1 .
  • Output: 1