Binary Search

Problem statement

A sorted shelf contains distinct integer catalogue codes. Locate the requested code by repeatedly narrowing the search range. Report its zero-based position, or -1 when the code is absent. Your search should take logarithmic time.

Input format

First line: n target. Second line: n distinct integers in strictly increasing order.

Output format

Print the zero-based index, or -1.

Constraints

1 <= n <= 100000; -1000000000 <= codes, target <= 1000000000.

Sample input

5 14
-6 2 7 14 20

Sample output

3