You are given a string s of length n and an integer array order, where order is a permutation of the numbers in the range [0, n - 1].

Starting from time t = 0, replace the character at index order[t] in s with '*' at each time step.

A substring is valid if it contains at least one '*'.

A string is active if the total number of valid substrings is greater than or equal to k.

Return the minimum time t at which the string s becomes active. If it is impossible, return -1.

 

Example 1:

Input: s = "abc", order = [1,0,2], k = 2

Output: 0

Explanation:

t order[t] Modified s Valid Substrings Count Active
(Count >= k)
0 1 "a*c" "*", "a*", "*c", "a*c" 4 Yes

The string s becomes active at t = 0. Thus, the answer is 0.

Example 2:

Input: s = "cat", order = [0,2,1], k = 6

Output: 2

Explanation:

t order[t] Modified s Valid Substrings Count Active
(Count >= k)
0 0 "*at" "*", "*a", "*at" 3 No
1 2 "*a*" "*", "*a", "*a*", "a*", "*" 5 No
2 1 "***" All substrings (contain '*') 6 Yes

The string s becomes active at t = 2. Thus, the answer is 2.

Example 3:

Input: s = "xy", order = [0,1], k = 4

Output: -1

Explanation:

Even after all replacements, it is impossible to obtain k = 4 valid substrings. Thus, the answer is -1.

 

Constraints: