Cross the Threshold

The final energy of each particle is max(energy−barrier,0). Find the largest non-negative integer barrier such that the total energy is ≥th. The original total energy is guaranteed to be ≥th.

输入格式

The first line contains n th, and the second line contains n energies. 2≤n≤100000, 1≤energy≤10⁹, 1≤th≤10¹⁴.

输出格式

Output the single integer required by the problem.

样例 1

输入：

5 9
4 8 7 2 1

输出：

3

样例 2

输入：

4 8
5 2 13 10

输出：

7

样例 3

输入：

3 6
3 9 7

输出：

5

样例说明

The answers to the three public examples are, in order: 3; 7; 5. All examples have been verified by independent small-scale enumeration or state search.