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Code Question 1

A manager at Amazon is responsible for organizing a thrilling online shopping event for a tech festival, and they have come up with an exciting concept. In this game, users are presented with a sequence of digits representing a product code. The challenge is to find a new product code that is equally attractive or even more attractive than the original one.

Let’s call an integer, represented in its decimal notation in order from left to right, b[1], b[2], b[3], ..., b[n] attractive if b[i] = b[i+k] for each i such that 1 ≤ i ≤ n - k, where n and k are positive integers. For example:

"252525" is attractive if k = 2
"245254" is not attractive.

Task:
Your task is to generate a new product code, represented by string new_code, such that it is greater than or equal to the original product code org_code.

Formal Definition:
Given a string org_code of size n representing the digits in the decimal notation and integer k, find a string new_code representing the digits in decimal notation, which satisfies:

old_code ≤ new_code
new_code is attractive, given that there are no leading zeroes in old_code and new_code.

Additional Details:
A string s of size n representing the digits in decimal notation is lexicographically less than string p of length m if one of the two statements is correct:

n < m and s is the beginning (prefix) of p.
s[1] = p[1], s[2] = p[2], ..., s[k-1] = p[k-1], and s[k] < p[k] for some k (1 ≤ k ≤ min(n, m)).

Here, characters in strings are numbered starting from 1.

Example

Input:

org_code = "1234"  
k = 2

Explanation:
Given org_code = "1234", where |org_code| = n = 4, and k = 2, the task is to find the smallest new_code such that:

It is greater than or equal to org_code, and
It satisfies the attractiveness condition (digits repeat every k positions).

Steps:

Take the first k digits from org_code ("12") and repeat them to form the candidate new_code = "1212".
Since "1212" is smaller than "1234", increment the first two digits, resulting in "13", and repeat it to get new_code = "1313".

Output:

new_code = "1313"

This new code is attractive because:

b[0] = b[2] = "1", and b[1] = b[3] = "3", and
It satisfies org_code ≤ new_code (as "1313" ≥ "1234").

Thus, "1313" is the required new_code.

Function Description

Complete the function findSmallestAppealing in the editor below.

findSmallestAppealing has the following parameters:

string old_code: integer old_code represented as a string in decimal notation.
int k: a positive integer such that k < n.

Returns:

string: smallest attractive integer new_code, such that old_code ≤ new_code, in decimal notation.

Constraints

1≤n≤2×1051 ≤ n ≤ 2 × 10^5
1≤k<n1 ≤ k < n
0≤orgcode[i]≤90 ≤ org_code[i] ≤ 9 for 0≤i<n0 ≤ i < n, and orgcode[0]≠0org_code[0] ≠ 0.

Sample Input 0