Maximum multiple of a number with all digits same

Given two positive integers X and Y (1 ? Y ? 10⁵), find the maximum positive multiple (say M) of X such that M is less than 10^Y and all the digits in the decimal representation of M are equal.

Note: If no positive multiple exists that satisfies the conditions, return -1.

Examples:

Input: X = 1, Y = 6
Output: 999999
Explanation: 999999 is the largest integer which is a multiple of 1, has all the same digits and less than 10⁶.

Input: X = 12, Y = 7
Output: 888888
Explanation: 888888 is the largest multiple of 12 which have all digits same and is less than 10⁷.

Input: X = 25, Y = 10
Output: -1
Explanation: No positive integers M satisfy the conditions.

Approach:

To solve the problem follow the below idea:

The main idea is to consider all the numbers less than 10^Y which have the same digits in decimal representation and check if the number is a multiple of X, from all such multiples, the maximum one as the result.

Step-by-step approach:

• Consider a function f(n, d) which denotes the remainder of the number with length n and all digits d when divided by X.
• Calculate f(n, d) for every {n, d}.
• Notice that f(n ? 1, d) is a prefix of f(n, d). So: f(n, d) = (f(n?1, d)*10 + d)%X
• Find the maximum value of n for which f(n, d) = 0. 
  • Choose the one with the maximum d among the ones with the maximum n.

Below is the implementation of the above approach.

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Time Complexity: O(Y)
Auxiliary Space: O(1)