Ninja and Numbers

Moderate

0/80

Average time to solve is 25m

Contributed by

5 upvotes

Problem statement

Ninja has a number ‘A’ containing ‘B’ digits. ‘A’ can be represented by a string ‘S’ where ‘S[i]’ denotes the ‘ith’ digit of ‘A’. You are also given an integer ‘K’.

Ninja thinks that a number is stable if the following condition is satisfied:

For every ‘ith’ digit where (0 <= ‘i’ <= ‘B-1’) ‘S[i] = S[i%K]’. Here, ‘X%Y’ represents the modulo operations. The remainder when ‘X’ is divided by ‘Y’.

Your task is to find the smallest number which is stable and whose value is greater than or equal to ‘A’. Zero-based indexing is used everywhere.

Example :

‘B’ = 4, ‘S’ = “4321”, ‘K’ = 3.
The given number is not stable as ‘S[3]’ is not the same as ‘S[0]’ but 3%3 = 0 same as 0%3. ‘S[3] = 1’ and ‘S[0] = 4’.  But the number “4324” is stable. As, for all ‘i’, ‘S[i]’ = ‘S[i%K]’ and “4324” is also greater than the given number. It can be proved that this is the best possible answer.
Hence, the answer is “4324”.

Detailed explanation ( Input/output format, Notes, Images )

Input Format :

The first line contains a single integer ‘T’ denoting the number of test cases, then the test case follows.

The first line of each test case contains two single space-separated integers, ‘B’ and ‘K'.
The second line contains a string with ‘B’ characters representing the string ‘S’.

Output Format :

For each test case, return the minimum stable number whose value is the same or exceeds the value of ‘A’.

Output for each test case will be printed on a separate line.

Note :

You are not required to print anything; it has already been taken care of. Just implement the function.

Constraints :

1 ≤ T ≤ 10
1 ≤ B ≤ 10^5
1 ≤ K ≤ 10^9
It’s guaranteed that sum of ‘B’ over all cases does not exceed 10^5. 
The given number will not contain leading zeros.

Time limit: 1 sec

Sample Input 1 :

Sample Output 1 :

6868
420

Explanation For Sample Input 1 :

For test case 1: 
6868 is the minimum possible, stable number. We can see that it is stable because ‘S[0] = S[2]’ because 0%2 = 2%2, and ‘S[1] = S[3]’ because 1%2 = 3%2. All the conditions are satisfied.
Hence, 6868 is the answer.

For test case 2:
The given number itself is stable, and hence it is the best possible answer.

Sample Input 2 :

Sample Output 2 :

44444
8585

Console