A. Orac and Factors
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

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.

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.

Example
Input
3
5 1
8 2
3 4

Output
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: $3 \to 6 \to 8 \to 10 \to 12$.