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

struct node {
  int n;
  struct node *left;
  struct node *right;
};


void push(struct node **root, int n) {
  struct node *p;
  if (!*root) {
    p = malloc(sizeof(struct node));
    p->n = n;
    p->left = p->right = NULL;
    *root = p;
    return;
  } 
  if (n != (*root)->n) {
    if (n < (*root)->n) {
      push(&((*root)->left), n);
    } else {
      push(&((*root)->right), n);
    }
  }
}

int pop(struct node **root) {
  struct node *p;
  int n;
  if (*root == NULL)
    return -1;
  if ((*root)->left)
    return pop(&((*root)->left));
  assert((*root)->left == NULL);
  p = *root;
  n = p->n;
  *root = p->right;
  free(p);
  return n;
}


#define N 9
int main() {
  int i, n, a, b, c;
  struct node *root = NULL;
  push(&root, 1);
  for (i = 0; i < N; i++) {
    n = pop(&root);
    a = 2 * n + 1; b = 3 * n + 1; c = 5 * n + 1;
    printf("%d: %d, %d, %d\n", n, a, b, c);
    push(&root, a);
    push(&root, b);
    push(&root, c);
  }
  while (pop(&root) > 0)
    ;
  return 0;
}
/* end */

1: 3, 4, 6
3: 7, 10, 16
4: 9, 13, 21
6: 13, 19, 31
7: 15, 22, 36
9: 19, 28, 46
10: 21, 31, 51
13: 27, 40, 66
15: 31, 46, 76