Prosti
Mirko and his older brother Slavko are playing a game. At the beginning of the game, they pick three numbers $K$, $L$, $M$. In the first and only step of the game, each of them picks their own $K$ consecutive integers.
Slavko always picks the first $K$ integers (numbers $1, 2, \ldots , K$). Mirko has a special demand—he wants to choose his numbers in a way that there are exactly $L$ happy numbers among them. He considers a number happy if it meets at least one of the following requirements:

the number is smaller than or equal to $M$

the number is prime
Out of respect to his older brother, $L$ will be smaller than or equal to the total number of happy numbers in Slavko’s array of numbers. They will play a total of $Q$ games with different values $K$, $L$, $M$. For each game, help Mirko find an array that meets his demand.
Input
The first line of input contains $Q$ ($1 \leq Q \leq 100\, 000$). Each of the following $Q$ lines contains three integers, the $i$th line containing integers $K_ i$, $L_ i$, $M_ i$ ($1 \leq K_ i, M_ i \leq 150$, $0 \leq L_ i \leq K_ i$) that determine the values $K$, $L$, $M$ that will be used in the $i$th game.
Output
Output $Q$ lines, the $i$th line containing an integer, the initial number of Mirko’s array in the $i$th game. If an array with the initial number being smaller than or equal to $10\, 000\, 000$ does not exist, output $1$. If there are multiple possible solutions, output any.
Sample Input 1  Sample Output 1 

3 1 1 1 2 0 2 3 1 1 
1 8 4 
Sample Input 2  Sample Output 2 

3 4 1 1 5 2 3 5 0 3 
6 4 24 
Sample Input 3  Sample Output 3 

4 7 2 5 6 1 1 10 4 5 6 2 2 
6 20 5 4 