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, \dots, 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 \le Q \le 100\,000)~. Each of the following ~Q~ lines contains three integers, the ~i^{th}~ line containing integers ~K_i, L_i, M_i~ ~(1 \le K_i, M_i \le 150, 0 \le L_i \le 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

3
1 1 1
2 0 2
3 1 1

Sample Output 1

1
8
4

Sample Input 2

3
4 1 1
5 2 3
5 0 3

Sample Output 2

6
4
24

Sample Input 3

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

Sample Output 3

6
20
5
4