/* Problem 3:  Phil Sweany's Consecutive Sum
   Given an integer, find all the consecutive sums leading to that
   integer. */

#include <stdio.h>
#include <stdlib.h>
#include <math.h>

int main (int argc, char **argv);

FILE *in, *out;

int main (int argc, char **argv) {

  int b, S, l; /* Beginning, sum, and length of a consecutive sum */

  /* This uses the formula for the sum of a consecutive 
     arithmetic sequence:   S = l/2 (2b+l-1), solving for b, S, and
     looping through all possible l's. */

 in = fopen ("prob3.in","r");
 out = fopen ("prob3.out","w");
 while (1) {
  fscanf (in,"%d",&S);
  if (S==0) break;
  for (l=sqrt (2*S); l > 1; l--) {  /* Solve for b */
   b = ((double)S/l + (1-l)/2.0) +0.5;
   if ((S%l==0 && l%2==1) || (S%l*2==l && l%2==0)) /*Is b an integer?*/
    fprintf (out,"%d %d\n",b,b+l-1);
  }
  fprintf (out,"\n");
 }
 fclose (in);
 fclose (out);
 return EXIT_SUCCESS;
}