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 1:


Input:
matrix = [
  [1,   3,  5,  7],
  [10, 11, 16, 20],
  [23, 30, 34, 50]
]
target = 3
Output: true


Example 2:


Input:
matrix = [
  [1,   3,  5,  7],
  [10, 11, 16, 20],
  [23, 30, 34, 50]
]
target = 13
Output: false

```python

USER_FILENAME = "<user_code>"
import sys, json, builtins
import math, heapq, bisect, itertools, functools, collections, statistics, fractions, decimal, operator, array, random, re, string, os, pathlib
try:
    import resource as _res
except Exception:
    _res = None
from collections import Counter, defaultdict, deque, OrderedDict
from functools import lru_cache, reduce
from itertools import accumulate, permutations, combinations, product
from math import gcd, ceil, floor, sqrt
from decimal import Decimal
try:
    from typing import *
except Exception:
    pass
try:
    sys.setrecursionlimit(1_000_000)
except Exception:
    pass
try:
    import site as _site
    try:
        _sys_sites = _site.getsitepackages() if hasattr(_site, "getsitepackages") else []
        for _p in _sys_sites:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
    try:
        _usp = _site.getusersitepackages()
        if isinstance(_usp, str):
            _usp = [_usp]
        for _p in _usp:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
except Exception:
    pass

def _disabled_input(*args, **kwargs):
    raise RuntimeError("input() is disabled in callable mode")
builtins.input = _disabled_input

ns = {"__name__": "__judge__"}  # prevent if __name__ == "__main__" blocks
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = "class Solution:\n     def findRow(self, matrix, target, l, h):\n         if l > h:\n             return -1\n         \n         elif l == h:\n             return h\n         \n         mid = l + int((h-l)/2)\n         \n         if matrix[mid][0] <= target <= matrix[mid][-1]:\n             return mid\n         elif matrix[l][0] <= target < matrix[mid][0]:\n             return self.findRow(matrix, target, l, mid-1)\n         else:\n             return self.findRow(matrix, target, mid+1, h)\n         \n     def bSearch(self, arr, target, l, h):\n         if l > h:\n             return -1\n         \n         mid = l + int((h-l)/2)\n         \n         if arr[mid] == target:\n             return mid\n         elif arr[l] <= target < arr[mid]:\n             return self.bSearch(arr, target, l, mid-1)\n         else:\n             return self.bSearch(arr, target, mid+1, h)\n     \n     def searchMatrix(self, matrix, target):\n         rows = len(matrix)\n         if rows == 0:\n             return False\n         cols = len(matrix[0])\n         \n         inRow = self.findRow(matrix, target, 0, rows-1)\n         print(('row present in %s' %inRow))\n         arr = matrix[inRow]\n         \n         index = self.bSearch(arr, target, 0, cols-1)\n         print(('present at index %s' %index))\n         \n         if index != -1:\n             return True\n         \n         return False\n         \n         \n"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'searchMatrix'
if _fn_name:
    if "Solution" in ns:
        try:
            _obj = ns["Solution"]()
            if hasattr(_obj, _fn_name):
                _target = getattr(_obj, _fn_name)
        except Exception:
            _target = None
    if _target is None and _fn_name in ns and callable(ns[_fn_name]):
        _target = ns[_fn_name]
# Fallback: if there's exactly one user-defined function, use it
if _target is None:
    _cands = [v for k, v in ns.items() if callable(v) and getattr(v, "__module__", "") in ("__judge__", "__main__")]
    _user_funcs = [c for c in _cands if getattr(c, "__name__", "").startswith("_") is False]
    if len(_user_funcs) == 1:
        _target = _user_funcs[0]
if _target is None:
    raise RuntimeError(f"Could not resolve callable '{_fn_name}'")

_raw = sys.stdin.read().strip()
if _raw:
    _parsed = json.loads(_raw)
    if isinstance(_parsed, dict):
        _kwargs = _parsed.get("kwargs", {})
        _args = _parsed.get("args", [])
    else:
        _args, _kwargs = _parsed, {}
else:
    _args, _kwargs = [], {}
if not isinstance(_args, (list, tuple)):
    _args = [_args]
_res = _target(*_args, **_kwargs)
try:
    sys.stdout.write(repr(_res) + "\n")
except Exception:
    pass

```

Measured memory_bytes: 6494