Search a 2D Matrix

Write an efficient algorithm that searches for a value in an m x n matrix. This matrix has the following properties:

• Integers in each row are sorted from left to right.
• The first integer of each row is greater than the last integer of the previous row.

Example:

Input

matrix = [
  [1, 3, 5, 7],
  [10, 11, 16, 20],
  [23, 30, 34, 60]
]
target = 3

Output

true

Input

matrix = [
  [1, 3, 5, 7],
  [10, 11, 16, 20],
  [23, 30, 34, 60]
]
target = 13

Output

false