Cyclic groups

Statement

Goal

Given an integer n and a character c, we define a Group of size n generated by c as the string set: 0, c, c * 2, ... , c * (n - 1). For example, 0 a aa aaa, generated by the element a, is a Group of size 4.

You are given an integer n, a character c and a string s, and you have to:

(1) If the string s represents a Group of size n generated by c, just print its size.
(2) If it isn't, print the NEEDED elements (ranged by string size) to make s a Group of size n.

Examples (the number n appears first):
3, 0 a aa   -> 3
3, 0 aa a   -> 3 (order is irrelevant)
4, 0 bbb b  -> bb (the only remaining for n = 4)
4, 0 c ccc  -> cc cccc
5, 0 c ccc  -> cc cccc ccccc

Input

Line 1: A positive integer n
Line 2: A character c
Line 3: A space separated string s representing the possible group to study.

Output

If s is a Group, it's size n.
If s is not a Group, a string with the NEEDED elements ranged by string size.

Constraints

c can be any ascii character.
First character in s is always 0.
0 < n < 10

Example

Input

3
a
0 a aa

Output

Game modes

Fastest, Shortest, Reverse

Test cases

1. Example Test

Input

3 a 0 a aa

Output

1. Example val Validator

Input

4 a 0 a aa aaa

Output

2. Not a group Test

Input

5 b 0 b bbbb

Output

bb bbb

2. Not a group val Validator

Input

7 c 0 c ccc cccc

Output

cc ccccc cccccc

3. Not a group (2) Test

Input

4 k 0 2 kkk o

Output

k kk

3. Not a group (2) val Validator

Input

7 k 0 A kk kkk kkkk < kkkkkk

Output

k kkkkk

4. Order doesn't matter Test

Input

6 & 0 & &&&&& && &&& &&&&

Output

4. Order doesn't matter val Validator

Input

9 & 0 & &&&&& && &&& &&&& &&&&&&&& &&&&&&& &&&&&&

Output

5. Extra Test

Input

6 Y 0 Y YYY YY Z

Output

YYYY YYYYY

5. Extra val Validator

Input

5 Z 0 ZZ Z Y YY YYY YYYY YYYYY

Output

ZZZ ZZZZ

6. Just zero Test

Input

3 ( 0

Output

( ((

6. Just zero val Validator

Input

4 ) 0

Output

) )) )))

Solution language

Solution

Stub generator input