A13386 | Orac and Factors

Orac is studying number theory, and he is interested in the properties of divisors.

For two positive integers $a$ and $b$ , $a$ is a divisor of $b$ if and only if there exists an integer $c$ , such that $a\cdot c=b$ .

For $n \ge 2$ , we will denote as $f(n)$ the smallest positive divisor of $n$ , except $1$ .

For example, $f(7)=7,f(10)=2,f(35)=5$ .

For the fixed integer $n$ , Orac decided to add $f(n)$ to $n$ .

For example, if he had an integer $n=5$ , the new value of $n$ will be equal to $10$ . And if he had an integer $n=6$ , $n$ will be changed to $8$ .

Orac loved it so much, so he decided to repeat this operation several times.

Now, for two positive integers $n$ and $k$ , Orac asked you to add $f(n)$ to $n$ exactly $k$ times (note that $n$ will change after each operation, so $f(n)$ may change too) and tell him the final value of $n$ .

For example, if Orac gives you $n=5$ and $k=2$ , at first you should add $f(5)=5$ to $n=5$ , so your new value of $n$ will be equal to $n=10$ , after that, you should add $f(10)=2$ to $10$ , so your new (and the final!) value of $n$ will be equal to $12$ .

Orac may ask you these queries many times.

The first line of the input is a single integer $t\ (1\le t\le 100)$ : the number of times that Orac will ask you.

Each of the next $t$ lines contains two positive integers $n,k\ (2\le n\le 10^6, 1\le k\le 10^9)$ , corresponding to a query by Orac.

It is guaranteed that the total sum of $n$ is at most $10^6$ .

Print $t$ lines, the $i$ -th of them should contain the final value of $n$ in the $i$ -th query by Orac.