PROSTI

문제

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, ..., 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.

입력

The first line of input contains Q (1 ≤ Q ≤ 100 000). Each of the following Q lines contains three integers, the i th line containing integers K_i, L_i, M_i (1 ≤ K_i, M_i ≤ 150, 0 ≤ L_i ≤ K_i) that determine the values K, L, M that will be used in the i th game.

출력

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.

3
1 1 1
2 0 2
3 1 1

1
8
4

3
4 1 1
5 2 3
5 0 3

6
4
24

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

6
20
5
4