Funny Number Game

Time limit0.5sMemory limit512 MB

Summary

Given a 4-digit N and M turns of incrementing one digit with 9 wrapping to 0, decide which player forces the final value above N.

Level: Hard8 of 10
Topics: Bit manipulation, Math, Game theory, Dynamic programming
Solved: No attempts yet

Problem

Koosaga and Cubelover play a "number game". The game proceeds as follows.

Choose a 4-digit integer $N$ and a number of turns $M$ .
Koosaga moves first, and the two players alternate turns.
On your turn, pick one digit of the integer and increase it by 1. If the chosen digit is 9, it becomes 0.

For example, 3590 can be changed to one of 4590, 3690, 3500, 3591. After the game ends, if the integer is greater than $N$ , Koosaga wins; otherwise Cubelover wins. Both players play optimally.

Given $N$ and $M$ , write a program that determines the winner.

Input

The first line contains a 4-digit integer $N$ and $M$ .

Output

Print koosaga if Koosaga wins, and cubelover if Cubelover wins.

Constraints

$0 \le N < 10^4$
$0 \le M \le 100$

Examples5

Example 1
Input
```
0000 0
```
Expected output
```
cubelover
```
Example 2
Input
```
5566 3
```
Expected output
```
koosaga
```
Example 3
Input
```
3333 10
```
Expected output
```
koosaga
```
Example 4
Input
```
9999 9
```
Expected output
```
cubelover
```
Example 5
Input
```
1234 30
```
Expected output
```
koosaga
```