#include <stdio.h>

#define SIZE 5

int lcm(int, int);
int gcd(int, int);
void swap(int&, int&);
void search(int *vals, int index, int lcm);

int main()
{
   int vals[SIZE];

   for(int n=2; n<SIZE; n++)
   {
      vals[0]=n;
      search(vals, 1, n);
   }
}

// currentLCM is the LCM of all values in the array before index
void search(int *vals, int index, int currentLCM)
{
   // Compute currentLCM/vals[0] + currentLCM/[1] + ...
   int sum = 0;
   for(int i=0; i<index; i++)
      sum += currentLCM/vals[i];
   if(currentLCM<=sum) return; // current sum is too big

   if(index==SIZE-1)
   {
      int rem = currentLCM - sum;
      if(currentLCM%rem == 0)
      {
         vals[SIZE-1] = currentLCM/rem;
         if(vals[SIZE-1] > vals[SIZE-2]) // don't allow a duplicate on the last value
         {
            for(int i=0; i<SIZE; i++)
               printf("%d ", vals[i]);
            printf("\n");
         }
      }
   }
   else
   {
      int minNext = vals[index-1] + 1;
      int valsLeft = SIZE - index;
      int maxNext = currentLCM * valsLeft / (currentLCM - sum);
      for(int i=minNext; i<=maxNext; i++)
      {
         vals[index] = i;
         search(vals, index+1, lcm(i, currentLCM));
      }
   }
}

// Finds lowest common multiple of two integers
int lcm(int x, int y)
{
   return x/gcd(x,y)*y;
}

// Finds gcd of two integers
int gcd(int x, int y)
{
   if(x<y) swap(x,y);
   if(y==0) return x;
   return gcd(x%y, y);
}

// Swap two integers sexily
void swap(int &x, int &y)
{
   x=x^y;
   y=x^y;
   x=x^y;
}