Background

"Because"? So what?

"Because I am your younger sister, you want me to tell you not to stop you from fooling around?"

"Because I am your younger sister, you want me to watch you go to your death?"

"Because I am your younger sister, you want me to silently watch you possibly get killed?"

"Stop kidding. What is this supposed to be? I thought peace had finally come with great difficulty, and I thought Shido would finally stop getting hurt."

"I—I do not want Shido to die. I do not want to see Shido get hurt again. I cannot stand letting Shido feel pain anymore..."

"Because I—"

"Like Shido—"

Problem Description

The annual International Saimoe League (ISML) has begun. As the former "Moe King", Kotori naturally does not need to participate. However, she wants to help her older brother Shido win the title of "Burning King".

In this ISML, there are $n=2^k$ contestants, numbered $1,2\ldots n$. Shido's number is $1$. The tournament is single-elimination. After each round, among the remaining contestants, the two with the smallest numbers become opponents, the $3$rd and $4$th smallest become opponents, and so on. The winner of a match is decided by fan votes: the side with more votes advances to the next round, and the side with fewer votes is eliminated.

For example, if there are $4$ contestants in total, then in the first round contestants $1$ and $2$ play a match, and contestants $3$ and $4$ play a match. Then the winners of the two matches play one more match to compete for the overall championship. The overall champion will receive the title of "Burning King".

Each character has a fan club. The number of members in contestant $i$'s fan club is $a_i$. In each round of voting, all fan club members will and will only vote for their corresponding contestant.

In addition, Kotori has a team of $m$ people, who will always follow Kotori's vote. That is, in every match, Kotori can add $m$ votes to either of the two contestants in that match. Note that in one round there may be multiple matches, and each match always has exactly two contestants.

Kotori also has a privilege: when the two sides have the same number of votes in a match, as the Moe King she can decide the winner of that match.

Now Kotori wants to know whether she has the ability to help her brother become the champion and obtain the title of "Burning King".

Input Format

This problem contains multiple test cases. The first line contains a positive integer $T$ indicating the number of test cases.

Then follow $T$ test cases. Each test case has two lines:

• The first line contains two integers $k,m$.
• The second line contains $2^k$ integers. The $i$-th integer denotes $a_i$.

Output Format

Output $T$ lines, one line for each test case.

For each test case, output Kotori if it can be done; otherwise output Yoshino.

3
3 6
2 0 0 5 0 9 0 9
3 6
2 0 5 0 0 5 0 9
2 6
2 0 0 5

Yoshino
Kotori
Kotori

Hint

[Sample Explanation #1]

For test case $1$, there is no plan that allows Shido to become the Burning King.

For test case $2$, consider the following plan:

Round $1$:

• Contestants $1$ and $2$ play. Give the votes to contestant $1$, and contestant $2$ is eliminated.
• Contestants $3$ and $4$ play. Give the votes to contestant $3$, and contestant $4$ is eliminated.
• Contestants $5$ and $6$ play. Give the votes to contestant $6$, and contestant $5$ is eliminated.
• Contestants $7$ and $8$ play. Give the votes to contestant $7$, and contestant $7$ is eliminated.

Round $2$:

• Contestants $1$ and $3$ play. Give the votes to contestant $1$, and contestant $3$ is eliminated.
• Contestants $6$ and $8$ play. Give the votes to contestant $6$, and contestant $8$ is eliminated.

Round $3$:

• Contestants $1$ and $6$ play. Give the votes to contestant $1$, and contestant $6$ is eliminated.

[Constraints and Conventions]

This problem uses bundled tests.

For $100\%$ of the data, $\sum n\le 2^{20}$, $0\le k\le 18$, and $0\le m,a_i\le 10^9$.

[Tips and Help]

The input size of this problem is relatively large. Please choose a faster input method.

The "world saimoe tournament" in this problem is different from the real "world saimoe tournament". In this problem, please follow this problem statement.

Translated by ChatGPT 5