I am stuck solving this problem asked in Amazon OA. Please help.

Given a binary string where missing values are denoted by *. Replace *s with 0s or 1s so as to achieve the minimum cost, given cost of having "01" every subsequence in string adds x and every subsequence "10" in string adds y to the final cost.

Test case are define as string, and numbers x and y respectively.

Constraints: size of string is 1 to 100000. x and y are from 0 to 100000.

Test cases :

Input1 01* 2 1

Output1: 3

Input2 !!!! 6 5

Output2: 0