#include <bits/stdc++.h>
using namespace std;
long long mod = 1e9 + 7;
int main() {
  long long a00, a01, a10, a11;
  cin >> a00 >> a01 >> a10 >> a11;
  long long x, y;
  x = 1 + sqrt(2LL * a11);
  y = 1 + sqrt(2LL * a00);
  if (x * (x - 1) != 2 * a11) {
    cout << "Impossible\n";
    return 0;
  }
  if (y * (y - 1) != 2 * a00) {
    cout << "Impossible\n";
    return 0;
  }
  if (a00 == 0 && a01 == 0 && a10 == 0 && a11 == 0) {
    cout << 1 << endl;
    return 0;
  }
  if (a01 == 0 && a10 == 0) {
    if (a00 && a11)
      cout << "Impossible\n";
    else {
      if (a00)
        for (int i = (1); i <= (y); i++) cout << "0";
      else
        for (int i = (1); i <= (x); i++) cout << "1";
    }
    return 0;
  }
  if ((a01 + a10) != x * y) {
    cout << "Impossible\n";
    return 0;
  }
  while (x + y) {
    if (a01 >= x)
      cout << '0', a01 -= x, y--;
    else
      cout << '1', a10 -= y, x--;
  }
  return 0;
}

### Prompt

In Cpp, your task is to solve 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;
long long mod = 1e9 + 7;
int main() {
  long long a00, a01, a10, a11;
  cin >> a00 >> a01 >> a10 >> a11;
  long long x, y;
  x = 1 + sqrt(2LL * a11);
  y = 1 + sqrt(2LL * a00);
  if (x * (x - 1) != 2 * a11) {
    cout << "Impossible\n";
    return 0;
  }
  if (y * (y - 1) != 2 * a00) {
    cout << "Impossible\n";
    return 0;
  }
  if (a00 == 0 && a01 == 0 && a10 == 0 && a11 == 0) {
    cout << 1 << endl;
    return 0;
  }
  if (a01 == 0 && a10 == 0) {
    if (a00 && a11)
      cout << "Impossible\n";
    else {
      if (a00)
        for (int i = (1); i <= (y); i++) cout << "0";
      else
        for (int i = (1); i <= (x); i++) cout << "1";
    }
    return 0;
  }
  if ((a01 + a10) != x * y) {
    cout << "Impossible\n";
    return 0;
  }
  while (x + y) {
    if (a01 >= x)
      cout << '0', a01 -= x, y--;
    else
      cout << '1', a10 -= y, x--;
  }
  return 0;
}

```