Description

You are a cafe barista. All coffees must have strength at least K to be served to customers. If there are weak coffees, blend the two weakest to make a stronger one. Blending formula: New coffee = weakest + (second weakest × 2) How many blendings are needed for all coffees to reach K?

Input

Output

Constraints

• •1 ≤ array length ≤ 1,000,000
• •0 ≤ strengths[i] ≤ 1,000,000
• •0 ≤ K ≤ 1,000,000,000

Examples

[1, 2, 3, 9, 10, 12], K = 7

2