#include <bits/stdc++.h>
using namespace std;
int n, a00, a01, a10, a11, x, y, z, now;
bool qwq;
int main() {
  scanf("%d%d%d%d", &a00, &a01, &a10, &a11);
  if (a00 == 0 && a11 == 0 && a01 == 0 && a10 == 0) return puts("0"), 0;
  a00 <<= 1, a11 <<= 1;
  if (a00 || a10 || a01)
    for (x = 1; x * (x - 1) < a00; x++)
      ;
  if (x * (x - 1) > a00) return puts("Impossible"), 0;
  if (a01 || a10 || a11)
    for (y = 1; y * (y - 1) < a11; y++)
      ;
  if (y * (y - 1) > a11) return puts("Impossible"), 0;
  if (x * y != a01 + a10) return puts("Impossible"), 0;
  while (x) {
    if (now + y > a10) break;
    z++, x--, now += y;
  }
  if (a10 - now) qwq = 1;
  for (int i = 0; i < x - qwq; i++) printf("0");
  for (int i = 0; i < a10 - now; i++) printf("1");
  if (qwq) printf("0");
  for (int i = a10 - now; i < y; i++) printf("1");
  for (int i = 0; i < z; i++) printf("0");
}

### Prompt

Generate a cpp solution to the following problem:

For each string s consisting of characters '0' and '1' one can define four integers a00, a01, a10 and a11, where axy is the number of subsequences of length 2 of the string s equal to the sequence {x, y}. 

In these problem you are given four integers a00, a01, a10, a11 and have to find any non-empty string s that matches them, or determine that there is no such string. One can prove that if at least one answer exists, there exists an answer of length no more than 1 000 000.

Input

The only line of the input contains four non-negative integers a00, a01, a10 and a11. Each of them doesn't exceed 109.

Output

If there exists a non-empty string that matches four integers from the input, print it in the only line of the output. Otherwise, print "Impossible". The length of your answer must not exceed 1 000 000.

Examples

Input

1 2 3 4


Output

Impossible


Input

1 2 2 1


Output

0110

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
int n, a00, a01, a10, a11, x, y, z, now;
bool qwq;
int main() {
  scanf("%d%d%d%d", &a00, &a01, &a10, &a11);
  if (a00 == 0 && a11 == 0 && a01 == 0 && a10 == 0) return puts("0"), 0;
  a00 <<= 1, a11 <<= 1;
  if (a00 || a10 || a01)
    for (x = 1; x * (x - 1) < a00; x++)
      ;
  if (x * (x - 1) > a00) return puts("Impossible"), 0;
  if (a01 || a10 || a11)
    for (y = 1; y * (y - 1) < a11; y++)
      ;
  if (y * (y - 1) > a11) return puts("Impossible"), 0;
  if (x * y != a01 + a10) return puts("Impossible"), 0;
  while (x) {
    if (now + y > a10) break;
    z++, x--, now += y;
  }
  if (a10 - now) qwq = 1;
  for (int i = 0; i < x - qwq; i++) printf("0");
  for (int i = 0; i < a10 - now; i++) printf("1");
  if (qwq) printf("0");
  for (int i = a10 - now; i < y; i++) printf("1");
  for (int i = 0; i < z; i++) printf("0");
}

```