#include <bits/stdc++.h>
int main() {
  long long a00, a01, a10, a11, c0, c1;
  std::cin >> a00 >> a01 >> a10 >> a11;
  c0 = (round(sqrt(8 * a00 + 1)) + 1) / 2;
  c1 = (round(sqrt(8 * a11 + 1)) + 1) / 2;
  if (!a01 && !a10) {
    if (!a00)
      c0 = 0;
    else
      c1 = 0;
  }
  if (c0 * (c0 - 1) / 2 != a00 || c1 * (c1 - 1) / 2 != a11 ||
      a01 + a10 != c0 * c1) {
    puts("Impossible");
    return 0;
  }
  while (c0 + c1)
    if (a01 >= c1) {
      putchar('0');
      a01 -= c1;
      --c0;
    } else {
      putchar('1');
      a10 -= c0;
      --c1;
    }
}

### Prompt

Develop a solution in cpp to the problem described below:

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>
int main() {
  long long a00, a01, a10, a11, c0, c1;
  std::cin >> a00 >> a01 >> a10 >> a11;
  c0 = (round(sqrt(8 * a00 + 1)) + 1) / 2;
  c1 = (round(sqrt(8 * a11 + 1)) + 1) / 2;
  if (!a01 && !a10) {
    if (!a00)
      c0 = 0;
    else
      c1 = 0;
  }
  if (c0 * (c0 - 1) / 2 != a00 || c1 * (c1 - 1) / 2 != a11 ||
      a01 + a10 != c0 * c1) {
    puts("Impossible");
    return 0;
  }
  while (c0 + c1)
    if (a01 >= c1) {
      putchar('0');
      a01 -= c1;
      --c0;
    } else {
      putchar('1');
      a10 -= c0;
      --c1;
    }
}

```