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# You are given a string num, representing a large integer. Return the largest-valued odd integer (as a string) that is a non-empty substring of num, or an empty string "" if no odd integer exists.
# A substring is a contiguous sequence of characters within a string.
# Example 1:
# Input: num = "52"
# Output: "5"
# Explanation: The only non-empty substrings are "5", "2", and "52". "5" is the only odd number.
# Example 2:
# Input: num = "4206"
# Output: ""
# Explanation: There are no odd numbers in "4206".
# Example 3:
# Input: num = "35427"
# Output: "35427"
# Explanation: "35427" is already an odd number.
# Constraints:
# 1 <= num.length <= 105
# num only consists of digits and does not contain any leading zeros.