/* Sun Mar 21 01:46:27 JST 2004 */
#include <stdio.h>
#include <string.h>
#include <limits.h>

#define max(x,y) (((x)>(y))?(x):(y))

int half(char *s)
{
  int i, j, len, q = 0;

  len = strlen(s);
  for (i = 0; i < len; i++) {
    s[i+1] += ((s[i]-'0')%2)*10;
    s[i  ]  = '0'+(s[i]-'0')/2;
  }
  if (s[0] == '0') {
    for (i = 0; i < len; i++) {
      s[i] = s[i+1];
    }
    len--;
  }
  if (s[len] > 0) { s[len] = '\0'; return 1; }
  return 0;
}

void dbl(char *s)
{
  int i, len;

  len = strlen(s);
  for (i = len-1; i >= 0; i--) {
    s[i] = '0'+((s[i]-'0')*2);
  }

  for (i = len-1; i >= 1; i--) {
    if (s[i] > '9') {
      s[i-1]++;
      s[i] = '0'+((s[i]-'0')%10);
    }
  }
  if (s[0] > '9') {
    for (i = len; i >= 0; i--) {
      s[i+1] = s[i];
    }
    len++;
    s[0] = '0'+((s[1]-'0')/10);
    s[1] = '0'+((s[1]-'0')%10);
  }
}

void inc(char *s)
{
  int i, len;

  len = strlen(s);
  s[len-1]++;

  for (i = len-1; i >= 1; i--) {
    if (s[i] > '9') {
      s[i] = '0';
      s[i-1]++;
    }
  }
  if (s[0] > '9') {
    for (i = len; i >= 0; i--) {
      s[i+1] = s[i];
    }
    len++;
    s[0] = '0'+((s[1]-'0')/10);
    s[1] = '0'+((s[1]-'0')%10);
  }
}

void swap(char *x, char *y)
{
  char t;
  t = *x;
  *x = *y;
  *y = t;
}

void reverse(char *s)
{
  int i, len;

  len = strlen(s);
  for (i = 0; i < len/2; i++) {
    swap(&s[i], &s[len-i-1]);
  }
}

void bit(char *s, char d[4096])
{
  int i;
  d[0] = '\0';
  for (i = 0; s[0] != '\0'; i++) {
    d[i] = (half(s) ? '1' : '0');
    d[i+1] = '\0';
  }
}

void encode(char *s, char d[1024])
{
  int i, len;
  len = strlen(s);
  strcpy(d, "0");
  for (i = 0; i < len; i++) {
    dbl(d);
    if (s[i] == '1') {
      inc(d);
    }
  }
}

void fill(char s[4096], int last)
{
  int i, len;

  len = strlen(s);
  for (i = len; i < last; i++) { s[i] = '0'; }
  s[last] = '\0';
}

char turn(char c)
{
  return '0'+(1-(c-'0'));
}

int cmp(char x[1024], char y[1024])
{
  int i, xlen, ylen, len;

  xlen = strlen(x);
  ylen = strlen(y);
  if (xlen < ylen) { return -1; }
  if (xlen > ylen) { return +1; }
  len = xlen = ylen;
  for (i = 0; i < len; i++) {
    if (x[i] < y[i]) { return -1; }
    if (x[i] > y[i]) { return +1; }
  }
  return 0;
}

unsigned int change(char x[4096], char y[4096], int f, char t[4096])
{
  int i, len;
  unsigned int count = 0;
  char s[4096];
  strcpy(s, x);

  len = strlen(x);
  t[len] = '\0';
  if (f) { s[0] = turn(s[0]); s[1] = turn(s[1]); t[0] = '1'; count++; }
  else   { t[0] = '0'; }
  for (i = 1; i < len; i++) {
    if (s[i-1] != y[i-1]) {
      s[i-1] = turn(s[i-1]);
      s[i  ] = turn(s[i  ]);
      if (i+1 < len) {
        s[i+1] = turn(s[i+1]);
      }
      t[i] = '1';
      count++;
    }
    else {
      t[i] = '0';
    }
  }

  if (s[len-1] != y[len-1]) { return UINT_MAX; }
  return count;
}

int main()
{
  char s[1024], *p, *q;
  char x[4096], y[4096], xlen, ylen, len;
  char a[4096], b[4096];
  char f[1024], g[1024];
  unsigned int m, n;
  int icase, result;

  for (icase = 1; ; icase++) {
    gets(s); p = strtok(s, " "); q = strtok(NULL, " ");
    if (strcmp(p, "0") == 0 && strcmp(q, "0") == 0) { break; }

    bit(p, x); xlen = strlen(x);
    bit(q, y); ylen = strlen(y);
    len = max(xlen, ylen);
    fill(x, len); fill(y, len);
    reverse(x); reverse(y);

    m = change(x, y, 0, a);
    encode(a, f);
    n = change(x, y, 1, b);
    encode(b, g);

    if (icase > 1) { printf("\n"); }
    printf("Case Number %d: ", icase);
    if (m == UINT_MAX && n == UINT_MAX) { printf("impossible\n"); }
    else if (m < n) { printf("%s\n", f); }
    else if (m > n) { printf("%s\n", g); }
    else if (cmp(f, g) < 0) { printf("%s\n", f); }
    else                    { printf("%s\n", g); }
  }
  return 0;
}