Tree Cutting

There are N trees standing in one row, and you need to take home at least M meters of wood in total.

If the cutter is set to height H, every tree taller than H is cut down to height H, and only the part above H is collected. Trees of height H or less are not cut. H may be any integer at least 0.

Find the maximum possible H that still lets you collect at least M meters of wood.

The first line contains the number of trees N and the required wood length M.

• 1 <= N <= 1,000,000
• 1 <= M <= 2,000,000,000

The second line contains the heights of the N trees. Each height is an integer from 0 to 1,000,000,000, inclusive. The sum of all tree heights is always at least M.

Print the maximum cutter height H that still lets you collect at least M meters of wood.