Orac and Factors
Description
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.
Input
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 $10^6$.
Output
Print $t$ lines, the $i$-th of them should contain the final value of $n$ in the $i$-th query by Orac.
Samples
3
5 1
8 2
3 4
10
12
12
Note
In the first query, $n=5$ and $k=1$. The divisors of $5$ are $1$ and $5$, the smallest one except $1$ is $5$. Therefore, the only operation adds $f(5)=5$ to $5$, and the result is $10$.
In the second query, $n=8$ and $k=2$. The divisors of $8$ are $1,2,4,8$, where the smallest one except $1$ is $2$, then after one operation $8$ turns into $8+(f(8)=2)=10$. The divisors of $10$ are $1,2,5,10$, where the smallest one except $1$ is $2$, therefore the answer is $10+(f(10)=2)=12$.
In the third query, $n$ is changed as follows: $3 \to 6 \to 8 \to 10 \to 12$.