Stairs to the Kimbap Heaven

Interview

Time limit1sMemory limit512 MB

Summary

Given N and K, decide whether Minhee can reach stair N in exactly K actions when tapping stair i moves Minhee to stair i + floor(i/2).

Level: Medium5 of 10
Topics: BFS, Shortest path
Solved: No attempts yet

Problem

Minhee wants to go to a heaven famous for its mini kimbap.

At the gate of heaven there are infinitely many stairs. The bottom stair is numbered 0, and the numbers increase by 1 as you go up. A kimbap shop is next to the $N$ -th stair.

Minhee can take a total of $K$ actions, choosing one of the following two actions each time. If Minhee reaches the $N$ -th stair exactly at the $K$ -th action, Minhee can eat mini kimbap.

Climb up one stair.
Tap the staff brought from home on the stair. If Minhee taps the staff on the $i$ -th stair, Minhee teleports to the $\left \lfloor \cfrac{i}{2} \right \rfloor$ stair above, that is, the $i +\left \lfloor \cfrac{i}{2} \right \rfloor$ -th stair.

Minhee is currently on the 0th stair. Find out whether Minhee can eat mini kimbap.

Input

The first line contains the number of stairs $N$ and the number of climbing actions $K$ . $(1 \leq N, K \leq 1\,000\,000)$

Output

If Minhee can eat mini kimbap by climbing the $N$ stairs in exactly $K$ actions, print minigimbob. Otherwise, if Minhee can only drink water, print water.

Hint

$\left \lfloor x \right \rfloor$ is the largest integer less than or equal to $x$ .

Examples2

Example 1
Input
```
5 2
```
Expected output
```
water
```
Example 2
Input
```
42 10
```
Expected output
```
minigimbob
```