An unfamiliar emotion arises. Will you scold me for this?

Yuki has her own aesthetic for numbers.

Yuki considers a positive integer $x$ to be "kawaii" if and only if the product of the digits of $x$ in its decimal representation is no greater than $k$.

For example, when $k=11$, $521$ is kawaii because $5\times2\times1=10 < 11$, while $314$ is not kawaii because $3\times1\times4=12 > 11$.

Now Yuki has $n$ positive integers $a_1, \dots, a_n$, where $1 \le a_i \le 10^{10^5}$. You need to determine whether each of them is kawaii. Note that $10^{10^5} = 10^{100000}$.

Although $a_i$ can be extremely large, Yuki believes that this will not be a problem for someone as clever as you!

Input

The first line contains two positive integers $n$ and $k$.

The next $n$ lines each contain a positive integer $a_i$.

Output

Output $n$ lines, where the $i$-th line contains a string:

• If $a_i$ is kawaii, output kawaii.
• If $a_i$ is not kawaii, output dame.

Examples

Input 1

4 8
15
24
37
80

Output 1

kawaii
kawaii
dame
kawaii

Note

In this example, $n=4$ and $k=8$.

• $15$ is kawaii because $1\times5=5 < 8$.
• $24$ is kawaii because $2\times4=8 = 8$.
• $37$ is not kawaii because $3\times7=21 > 8$.
• $80$ is kawaii because $8\times0=0 < 8$.

Input 2

3 998244353
31415926535
9999999999
17320508075

Output 2

kawaii
dame
kawaii

Note

In this example, $n=3$ and $k=998244353$.

• $31415926535$ is kawaii because the product of its digits in decimal representation is $486000$, which is less than $998244353$.
• $9999999999$ is not kawaii because the product of its digits in decimal representation is $3486784401$, which is greater than $998244353$.
• $17320508075$ is kawaii because the product of its digits in decimal representation is $0$, which is less than $998244353$.

Input 3

(See problem attachments)

Output 3

(See problem attachments)

Note

This sample satisfies the constraints for test case 4.

Input 4

(See problem attachments)

Output 4

(See problem attachments)

Note

This sample satisfies the constraints for test case 7.

Input 5

(See problem attachments)

Output 5

(See problem attachments)

Note

This sample satisfies the constraints for test case 10.

Constraints

For all test data:

• $1 \le n \le 20$
• $1 \le k \le 10^9$
• $1 \le a_i \le 10^{10^5}$

Special Property: $a_i$ is guaranteed not to contain the digit $0$ in its decimal representation.