Gorodetskiy is a university student. He is really good at math and really likes solving engaging math problems. In the last exam, his professor gave him really hard math problems to solve, but Gorodetskiy could not solve them and failed the exam, so the professor told him: "These problems are a piece of cake, you should know them from school!" Here is one of the problems from the exam - you can decide if it really was an easy problem or not.
You are given a positive integer $M$. Let's call a positive integer $A$ an interesting number if there is at least one integer $B$ ($A \le B$) such that $A \cdot B$ is divisible by $M$ and $\frac{A \cdot B}{M} = A+B$.
Find all interesting numbers. Let's denote the number of such integers by $K$; it is guaranteed that $K \le 3*10^5$.

-----Input-----
- The first line of the input contains a single integer $T$ denoting the number of test cases. The description of $T$ test cases follows.
- The first and only line of each test case contains a single integer $M$.

-----Output-----
For each test case:
- First, print a line containing a single integer $K$.
- Then, print $K$ lines. For each valid $i$, the $i$-th of these lines should contain a single integer ― the $i$-th interesting number in increasing order.

-----Constraints-----
- $1 \le T \le 10$
- $1 \le M \le 10^{14}$

-----Subtasks-----
Subtask #1 (20 points): $1 \le M \le 100$
Subtask #2 (20 points): $1 \le M \le 10^7$
Subtask #3 (60 points): original constraints

-----Example Input-----
2
3
6

-----Example Output-----
2
4
6
5
7
8
9
10
12

-----Explanation-----
Example case 1: There are two interesting numbers, $4$ and $6$. For $A = 4$, we can choose $B = 12$ and for $A = 6$, we can choose $B = 6$.

Difficulty: interview

Starter code:

Solutions:

def interesting_nums(m):
 nums = []
 for x in range(m + 1, 2 * m + 1):
  if x * m % (x - m) == 0:
   nums.append(x)

 return nums


def main():

 T = int(input())

 for _ in range(T):
  num_list = interesting_nums(int(input()))
  print(len(num_list))

  for num in num_list:
   print(num)


main()


def interesting_nums(m):
 nums = []
 for x in range(m + 1, 2 * m + 1):
  if x * m % (x - m) == 0:
   nums.append(x)

 return nums


def main():

 T = int(input())

 for _ in range(T):
  num_list = interesting_nums(int(input()))
  print(len(num_list))

  for num in num_list:
   print(num)


main()


t=int(input())
m=[int(input()) for i in range(t)]
print("")
for i in m:
 arr=[]
 count=0
 for a in range(i+1,i*2+1):
  inpX=(i*a)/(a-i)
  if inpX>=a and (i*a)%(a-i)==0:
   count=count+1
   arr.append(a)
 print(count)
 for j in arr:
  print(j)
 



t=int(input())
m=[int(input()) for i in range(t)]
for i in m:
 c=0
 ANS=[]
 for a in range(i+1,2*i+1,1):
  intp=a*i/(a-i)
  if intp>=a and a*i%(a-i)==0:
   c=c+1
   ANS.append(a)
 print(c)
 for j in ANS:
  print(j)


import sys 
 
sys.setrecursionlimit(10**8) 
t=int(input())
m=[int(input()) for i in range(t)]

 
def rec(a,m,list1):

 b=a*m/(a-m)
 if b>=a and a*m%(a-m)==0 and a<=2*m:
  
  list1.append(a)
  a=a+1
  
  rec(a,m,list1)
  
 else:
  if a<=2*m:
   a=a+1
 
   rec(a,m,list1)
   
  
 
 
for i in m:
 c=0
 
 
 a=i+1
 ANS=[]
 rec(a,i,ANS)
 
 print(len(ANS))
 ANS.sort()
 for j in ANS:
  print(j)
    
   
    
    


import sys 
 
sys.setrecursionlimit(10**8) 
t=int(input())
m=[int(input()) for i in range(t)]

 
def rec(a,m,list1):

 b=a*m/(a-m)
 if b>=a and a*m%(a-m)==0 and a<=2*m:
  
  list1.append(a)
  a=a+1
  
  rec(a,m,list1)
  
 else:
  if a<=2*m:
   a=a+1
 
   rec(a,m,list1)
   
  
 
 
for i in m:
 c=0
 
 
 a=i+1
 ANS=[]
 rec(a,i,ANS)
 
 print(len(ANS))
 ANS.sort()
 for j in ANS:
  print(j)
    
   
    
    


t=int(input())
m=[int(input()) for i in range(t)]
 
for i in m:
 c=0
 ANS=[]
 if i%2!=0:
  for a1 in range(i+1,2*i+1,2):
   intp=a1*i/(a1-i)
   if intp>=a1 and a1*i%(a1-i)==0:
    c=c+1
    ANS.append(a1)
 
 else:
  for a1 in range(i+1,2*i+1,1):
   intp=a1*i/(a1-i)
   if intp>=a1 and a1*i%(a1-i)==0:
    c=c+1
   
    ANS.append(a1)
 
 ANS.sort()
 
 print(c)
 for j in ANS:
  print(j)
    
   
    
    


from math import sqrt
def sol(p, m):
 if p == s:
  ans.append(m + N)
  return
 __pow = 1
 for i in range(ls[p][1] + 1):
  if m > N // __pow:break
  sol(p + 1, m * __pow)
  __pow *= ls[p][0]
for _ in range(int(input())):
 n = int(input())
 N, sq,ls,ans = n, int(sqrt(n)),list(),list()
 for i in range(2, sq+1):
  if n % i == 0:
   Count = 0
   while n % i == 0:
    Count += 2
    n //= i
   ls.append([i, Count])
 if n != 1:ls.append([n, 2])
 s = len(ls)
 sol(0, 1)
 ans.sort()
 print(len(ans))
 print(*ans, sep = '\n')


# cook your dish here
from math import sqrt
def sol(p, m):
 if p == s:
  ans.append(m + N)
  return
 __pow = 1
 for i in range(ls[p][1] + 1):
  if m > N // __pow:break
  sol(p + 1, m * __pow)
  __pow *= ls[p][0]
for _ in range(int(input())):
 n = int(input())
 N, sq,ls,ans = n, int(sqrt(n)),list(),list()
 for i in range(2, sq+1):
  if n % i == 0:
   Count = 0
   while n % i == 0:
    Count += 2
    n //= i
   ls.append([i, Count])
 if n != 1:ls.append([n, 2])
 s = len(ls)
 sol(0, 1)
 ans.sort()
 print(len(ans))
 print(*ans, sep = '\n')

from math import sqrt
def sol(p, m):
 if p == s:
  ans.append(m + N)
  return
 __pow = 1
 for i in range(ls[p][1] + 1):
  if m > N // __pow:break
  sol(p + 1, m * __pow)
  __pow *= ls[p][0]
for _ in range(int(input())):
 n = int(input())
 N, sq,ls,ans = n, int(sqrt(n)),list(),list()
 for i in range(2, sq+1):
  if n % i == 0:
   Count = 0
   while n % i == 0:
    Count += 2
    n //= i
   ls.append([i, Count])
 if n != 1:ls.append([n, 2])
 s = len(ls)
 sol(0, 1)
 ans.sort()
 print(len(ans))
 print(*ans, sep = '\n')


from math import sqrt
def sol(p, m):
 if p == s:
  ans.append(m + N)
  return
 __pow = 1
 for i in range(ls[p][1] + 1):
  if m > N // __pow:break
  sol(p + 1, m * __pow)
  __pow *= ls[p][0]
for _ in range(int(input())):
 n = int(input())
 N, sq,ls,ans = n, int(sqrt(n)),list(),list()
 for i in range(2, sq+1):
  if n % i == 0:
   Count = 0
   while n % i == 0:
    Count += 2
    n //= i
   ls.append([i, Count])
 if n != 1:ls.append([n, 2])
 s = len(ls)
 sol(0, 1)
 ans.sort()
 print(len(ans))
 print(*ans, sep = '\n')

# cook your dish here
for i in range(int(input())):
 m=int(input())
 l=[]
 p=m**2 
 ans=0
 for i in range(1,m+1):
  if(p%i==0):
   ans+=1 
   l.append(i+m)
 print(ans)
 for i in l:
  print(i)

n =[]
for i in range(int(input())):
 n.append(int(input()))
for m in n:
 r=[]
 c=0
 for a in range(m+1, 2*m+1):
  b = (a*m)//(a-m)
  if (a*b%m==0):
   c+=1
   r.append(a)
 print(c)
 for a in r:
  print(a)

# cook your dish here
from math import sqrt
def prime_facs(n):
 l=[1]
 for i in range(2,int(sqrt(n))+1):
  if n%i==0:
   l.append(i)
 return l
for a0 in range(int(input())):
 n=int(input())
 x=prime_facs(n**2)
 print(len(x))
 for i in x:
  print(i+n)


from math import sqrt
def sol(p, m):
 if p == s:
  ans.append(m + N)
  return
 __pow = 1
 for i in range(ls[p][1] + 1):
  if m > N // __pow:
   break
  sol(p + 1, m * __pow)
  __pow *= ls[p][0]

for _ in range(int(input())):
 n = int(input())
 N, sq = n, int(sqrt(n))
 ls = list()
 ans = list()
 for i in range(2, sq+1):
  if n % i == 0:
   Count = 0
   while n % i == 0:
    Count += 2
    n //= i
   ls.append([i, Count])
 if n != 1:
  ls.append([n, 2])
 s = len(ls)
 sol(0, 1)
 ans.sort()
 print(len(ans))
 print(*ans, sep = '\n')


# cook your dish here
for i in range(int(input())):
 m=int(input())
 l=[]
 p=m**2 
 ans=0
 for i in range(1,m+1):
  if(p%i==0):
   ans+=1 
   l.append(i+m)
 print(ans)
 for i in l:
  print(i)


T = int(input())

for t in range(T):
 M = int(input())
 A = []
 for a in range(M+1, 2*M+1):
  b = (a*M)/(a-M)
  if float(a+b).is_integer() == True and a <= b:
   A.append(a)

 print(len(A))
 for i in range(len(A)):
  print(A[i])




T = int(input())

for t in range(T):
 M = int(input())
 A = []
 for a in range(M+1, 2*M+1):
  if float((a*a)/(a-M)).is_integer() == True and (a*M)/(a-M) > 0:
   A.append(a)

 print(len(A))
 for i in range(len(A)):
  print(A[i])

T = int(input())

for t in range(T):
 M = int(input())
 A = []
 for a in range(M+1, 2*M+1):
  b = (a*M)/(a-M)
  if float(a+b).is_integer() == True and b > 0:
   A.append(a)

 print(len(A))
 for i in range(len(A)):
  print(A[i])



T = int(input())

for t in range(T):
 M = int(input())
 A = []
 for a in range(2*M+1):
  if a != M:
   b = (a*M)/(a-M)
   if (a*b) % M == 0 and b > 0:
    A.append(a)
 print(len(A))
 for i in range(len(A)):
  print(A[i])

import sys
sys.setrecursionlimit(10**9)
t=int(input())
prime=[]
ind=2
aa=[-1]*(10**7+5)
def func(ind,prod):
 nonlocal p,ss,ll
 if ind==len(p) :
  ll.append(prod)
  return ''
 po=prod
 for i in range(p[ind][1]+1):
  #  print(po,i,ind)
  if po>m:
   break
  func(ind+1,po)
  po*=p[ind][0]
 
 
 
while ind<10**7+5:
 if aa[ind-1]==-1:
  prime.append(ind)
  aa[ind-1::ind]=[0]*len(aa[ind-1::ind])
 ind+=1
 
for _ in range(t):
 m=int(input())
 p=[]
 ind=0
 mm=int(m**0.5)
 n=m
 while prime[ind]<=mm+1:
  count=0
  while True:
   if n%prime[ind]==0:
    count+=2
    n//=prime[ind]
   else:
    break
  if count>0:
   p.append([prime[ind],count])
  ind+=1
  if ind==len(prime):
   break
 if n!=1:
  p.append([n,2])

 # print(p)
 ss=[]
 ll=[]
 
 func(0,1)
 ll.sort()
 print(len(ll))
 for i in ll:
  print(i+m)
 
   


import sys
sys.setrecursionlimit(10**9)
t=int(input())
prime=[]
ind=2
aa=[-1]*(10**4)
def func(ind,prod):
 nonlocal p,ss,ll
 if ind==len(p) :
  ll.append(prod)
  return ''
 po=prod
 for i in range(p[ind][1]+1):
  #  print(po,i,ind)
  if po>m:
   break
  func(ind+1,po)
  po*=p[ind][0]
 
 
 
while ind<10**4:
 if aa[ind-1]==-1:
  prime.append(ind)
  aa[ind-1::ind]=[0]*len(aa[ind-1::ind])
 ind+=1
 
for _ in range(t):
 m=int(input())
 p=[]
 ind=0
 mm=int(m**0.5)
 n=m
 while prime[ind]<=mm+1:
  count=0
  while True:
   if n%prime[ind]==0:
    count+=2
    n//=prime[ind]
   else:
    break
  if count>0:
   p.append([prime[ind],count])
  ind+=1
  if ind==len(prime):
   break
 if n!=1:
  p.append([n,2])

 # print(p)
 ss=[]
 ll=[]
 
 func(0,1)
 ll.sort()
 print(len(ll))
 for i in ll:
  print(i+m)
 
   


import sys
sys.setrecursionlimit(10**9)
t=int(input())
prime=[]
ind=2
aa=[-1]*(10**4)
def func(ind,prod):
 nonlocal p,ss,ll
 if ind==len(p) :
  ll.append(prod)
  return ''
 po=prod
 for i in range(p[ind][1]+1):
  #  print(po,i,ind)
  if po>m:
   break
  func(ind+1,po)
  po*=p[ind][0]
 
 
 
while ind<10**4:
 if aa[ind-1]==-1:
  prime.append(ind)
  aa[ind-1::ind]=[0]*len(aa[ind-1::ind])
 ind+=1
 
for _ in range(t):
 m=int(input())
 p=[]
 ind=0
 mm=int(m**0.5)
 n=m
 while prime[ind]<=mm+1 and ind<len(prime):
  count=0
  while True:
   if n%prime[ind]==0:
    count+=2
    n//=prime[ind]
   else:
    break
  if count>0:
   p.append([prime[ind],count])
  ind+=1
 if n!=1:
  p.append([n,2])

 # print(p)
 ss=[]
 ll=[]
 
 func(0,1)
 ll.sort()
 print(len(ll))
 for i in ll:
  print(i+m)
 
   


import sys,math
sys.setrecursionlimit(10**9)
t=int(input())
prime=[]
ind=2
aa=[-1]*(10**4)
def func(ind,prod):
 nonlocal p,ss,ll
 if ind==len(p) :
  ll.append(prod)
  return ''
 po=prod
 for i in range(p[ind][1]+1):
  #  print(po,i,ind)
  if po>m:
   break
  func(ind+1,po)
  po*=p[ind][0]
 
 
 
while ind<10**4:
 if aa[ind-1]==-1:
  prime.append(ind)
  aa[ind-1::ind]=[0]*len(aa[ind-1::ind])
 ind+=1
 
for _ in range(t):
 m=int(input())
 p=[]
 ind=0
 mm=int(m**0.5)
 n=m
 for i in range(2,int(math.sqrt(m))+1):
  if n % i == 0:
   Count = 0
   while n % i == 0:
    Count += 2
    n //= i
   p.append([i, Count])
 if n!=1:
  p.append([n,2])

 # print(p)
 ss=[]
 ll=[]
 
 func(0,1)
 ll.sort()
 print(len(ll))
 for i in ll:
  print(i+m)
 
   


import sys
sys.setrecursionlimit(10**9)
t=int(input())
prime=[]
ind=2
aa=[-1]*(10**4)
def func(ind,prod):
 nonlocal p,ss,ll
 if ind==len(p) :
  ll.append(prod)
  return ''
 po=prod
 for i in range(p[ind][1]+1):
  #  print(po,i,ind)
  if po>m:
   break
  func(ind+1,po)
  po*=p[ind][0]
 
 
 
while ind<10**4:
 if aa[ind-1]==-1:
  prime.append(ind)
  aa[ind-1::ind]=[0]*len(aa[ind-1::ind])
 ind+=1
 
for _ in range(t):
 m=int(input())
 p=[]
 ind=0
 mm=int(m**0.5)
 n=m
 while prime[ind]<=mm+1:
  count=0
  while True:
   if n%prime[ind]==0:
    count+=2
    n//=prime[ind]
   else:
    break
  if count>0:
   p.append([prime[ind],count])
  ind+=1
 if n!=1:
  p.append([n,2])

 # print(p)
 ss=[]
 ll=[]
 
 func(0,1)
 ll.sort()
 print(len(ll))
 for i in ll:
  print(i+m)