Happy Numbers

Junhyung and Minhyung play a sequence game. Before the game starts, Minhyung picks three numbers $K$, $L$, and $M$. Junhyung then has to say $K$ consecutive natural numbers.

Minhyung added one more rule to train Junhyung's mental arithmetic. Among the $K$ numbers Junhyung says, exactly $L$ of them must be happy numbers. A happy number is a number that meets at least one of the two conditions below.

• It is a natural number not greater than $M$.
• It is a prime (a number with exactly 2 divisors).

Junhyung is slow at mental arithmetic, so he plans to work the answer out on a computer in secret. Write a program that answers Minhyung's questions.

The first line contains the number of test cases $Q$ ($1 \le Q \le 100\,000$).

Each of the next $Q$ lines contains $K$, $L$, and $M$. ($1 \le K, M \le 150$, $0 \le L \le K$)

For each test case, print on one line the smallest of the $K$ numbers Junhyung says, that is, the starting value of the run of $K$ consecutive natural numbers. If several starting values satisfy the condition, print the smallest one. If no starting value satisfies the condition, or the smallest one is greater than 10,000,000, print -1.