Problem Description

ztr love reserach substring.Today ,he has n string.Now ztr want to konw,can he take out exactly k palindrome from all substring of these n string,and thrn sum of length of these k substring is L.

for example string "yjqqaq"
this string contains plalindromes:"y","j","q","a","q","qq","qaq".
so we can choose "qq" and "qaq".

Input

The first line of input contains an positive integer $T(T<=10)$ indicating the number of test cases.

For each test case:

First line contains these positive integer $N(1<=N<=100),K(1<=K<=100),L(L<=100)$.
The next N line,each line contains a string only contains lowercase.Guarantee even length of string won't more than L.

Output

For each test,Output a line.If can output "True",else output "False".

3
2 3 7
yjqqaq
claris
2 2 7
popoqqq
fwwf
1 3 3
aaa

False
True
True