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⋅ c=b.

For n ≥ 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≤ t≤ 100): the number of times that Orac will ask you.

Each of the next t lines contains two positive integers n,k\ (2≤ n≤ 10^6, 1≤ k≤ 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 → 6 → 8 → 10 → 12.
from math import *
from copy import *
from string import *				# alpha = ascii_lowercase
from random import *
from sys import stdin
from sys import maxsize
from operator import *				# d = sorted(d.items(), key=itemgetter(1))
from itertools import *
from collections import Counter		# d = dict(Counter(l))
import math
import math
import time

def bin1(l,r,k,t,b,val,ans):
	if(l>r):
		return ans
	else:
		mid=(l+r)//2
		v=k**mid
		if(v==val):
			return v
		elif(v>val):
			ans=mid
			return bin1(mid+1,r,k,t,b,val,ans)
		else:
			return bin1(l,mid-1,k,t,b,val,ans)
		
def bin2(l,r,k,t,b,val,ans):
	if(l>r):
		return ans
	else:
		mid=(l+r)//2
		v=t*(k**mid)+b*(mid)
		if(v==val):
			return v
		elif(v>val):
			ans=mid
			return bin2(l,mid-1,k,t,b,val,ans)
		else:
			return bin2(mid+1,r,k,t,b,val,ans)

def SieveOfEratosthenes(n): 
      
    # Create a boolean array "prime[0..n]" and initialize 
    #  all entries it as true. A value in prime[i] will 
    # finally be false if i is Not a prime, else true. 
    prime = [-1 for i in range(n+1)] 
    p = 2
    while (p * p <= n): 
          
        # If prime[p] is not changed, then it is a prime 
        if (prime[p] == -1): 
              
            # Update all multiples of p 
            for i in range(p * p, n+1, p): 
                prime[i] = p
        p += 1
    for i in range(2,n+1):
    	if(prime[i]==-1):
    		prime[i]=i
    return prime
def bin(l,r,ll,val):
	if(l>r):
		return -1
	else:
		mid=(l+r)//2
		if(val>=ll[mid][0] and val<=ll[mid][1]):
			return mid
		elif(val<ll[mid][0]):
			return bin(l,mid-1,ll,val)
		else:
			return bin(mid+1,r,ll,val)
def deci(n):
	s=""
	while(n!=0):
		if(n%2==0):
			n=n//2
			s="0"+s
		else:
			n=n//2
			s="1"+s
	return s
def diff(s1,s2):
	if(len(s1)<len(s2)):
		v=len(s1)
		while(v!=len(s2)):
			s1="0"+s1
			v=v+1
	else:
		v=len(s2)
		while(v!=len(s1)):
			s2="0"+s2
			v=v+1
	c=0
	for i in range(len(s1)):
		if(s1[i:i+1]!=s2[i:i+1]):
			c=c+1
	return c
from sys import stdin, stdout 
def fac(a,b):
	v=a
	while(a!=b):
		v*=a-1
		a=a-1
	return v
def bino(l,r,n):
	if(l>r):
		return -1
	else:
		mid=(l+r)//2
		val1=math.log((n/mid)+1,2)
		val2=int(val1)
		if(val1==val2):
			return val1
		elif(val1<1.0):
			return bino(l,mid-1,n)
		else:
			return bino(mid+1,r,n)

def binary(l,r,val,ans):
	if(l>r):
		return -1
	else:
		mid=(l+r)//2
		v=val**5-mid**5
		print(v)
		if(v==ans):
			print("HOHOHOH")
			return mid
		elif(v<ans):
			return binary(mid+1,r,val,ans)
		else:
			return binary(l,mid-1,val,ans)
def check(n):
	v=1
	while(n!=0):
		if(n%10==0 or n%10==1):
			n=n//10
		else:
			v=0
			break
	return v
def stairs(n,m,val,c,l):
	if(val>n):
		return 100000
	elif(val==n):
		if(l[val]!=-1):
			return l[val]
		elif(c%m==0):
			l[val]=c
			return l[val];
		else:
			l[val]=100000
			return l[val]
	else:
		# if(l[val]!=-1):
		# 	return l[val]
		# else:
		l[val]=min(stairs(n,m,val+1,c+1,l),stairs(n,m,val+2,c+1,l))
		return l[val]
def fact(n):
	if(n==0 or n==1):
		return 1
	else:
		return n*fact(n-1)

def some(n):
	s=0
	while(n!=0):
		s+=fact(n%10)
		n//=10
	return s
def bin(l,r,val,ll):
    if(l>r):
        return -1
    else:
        mid=(l+r)//2
        if(ll[mid]==val):
            return mid
        elif(ll[mid]>val):
            return bin(l,mid-1,val,ll)
        else:
            return bin(mid+1,r,val,ll)
def fn(n):
	c=-1
	for i in range(2,int(sqrt(n))+1):
		if(n%2==0):
			c=i
			break
	if(c==-1):
		c=n
	return c

if __name__ == '__main__':
	l=SieveOfEratosthenes(1000000)
	t=int(input())
	for i in range(t):
		n,k=map(int,input().split(" "))
		val=0
		for j in range(2,n+1):
			if(n%j==0):
				val=j
				break
		print(n+val+(k-1)*2)