#include <bits/stdc++.h>
using namespace std;
int main() {
  long long a00, a01, a10, a11;
  cin >> a00 >> a01 >> a10 >> a11;
  if (!a00 && !a01 && !a10 && !a11) {
    cout << "1\n";
    return 0;
  }
  long long k1, k2;
  k1 = sqrt(2 * a00) + 1;
  if (k1 * (k1 - 1) != a00 * 2) {
    cout << "Impossible\n";
    return 0;
  }
  k2 = sqrt(2 * a11) + 1;
  if (k2 * (k2 - 1) != a11 * 2) {
    cout << "Impossible\n";
    return 0;
  }
  if (k1 == 1 && k2 == 1) {
    if (a10 == 0 && a01 == 1) {
      printf("01");
      return 0;
    } else if (a10 == 1 && a01 == 0) {
      printf("10");
      return 0;
    } else if (a10 == 0 && a01 == 0) {
      printf("1");
      return 0;
    } else {
      printf("Impossible");
      return 0;
    }
  } else if (k1 == 1) {
    if (a10 + a01 == 0) {
      k1 = 0;
      for (int i = 1; i <= k2; i++) printf("1");
      return 0;
    }
  } else if (k2 == 1) {
    if (a01 + a10 == 0) {
      k2 = 0;
      for (int i = 1; i <= k1; i++) printf("0");
      return 0;
    }
  }
  if (a10 + a01 != k1 * k2) {
    cout << "Impossible\n";
    return 0;
  }
  long long m = a10 / k1, n = a10 % k1;
  k2 -= m;
  string s;
  for (int i = 0; i < m; i++) s += '1';
  for (int i = k1; i > 0; i--) {
    if (i == n) {
      s += '1';
      k2--;
    }
    s += '0';
  }
  for (int i = 0; i < k2; i++) s += '1';
  cout << s;
}

### 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 main() {
  long long a00, a01, a10, a11;
  cin >> a00 >> a01 >> a10 >> a11;
  if (!a00 && !a01 && !a10 && !a11) {
    cout << "1\n";
    return 0;
  }
  long long k1, k2;
  k1 = sqrt(2 * a00) + 1;
  if (k1 * (k1 - 1) != a00 * 2) {
    cout << "Impossible\n";
    return 0;
  }
  k2 = sqrt(2 * a11) + 1;
  if (k2 * (k2 - 1) != a11 * 2) {
    cout << "Impossible\n";
    return 0;
  }
  if (k1 == 1 && k2 == 1) {
    if (a10 == 0 && a01 == 1) {
      printf("01");
      return 0;
    } else if (a10 == 1 && a01 == 0) {
      printf("10");
      return 0;
    } else if (a10 == 0 && a01 == 0) {
      printf("1");
      return 0;
    } else {
      printf("Impossible");
      return 0;
    }
  } else if (k1 == 1) {
    if (a10 + a01 == 0) {
      k1 = 0;
      for (int i = 1; i <= k2; i++) printf("1");
      return 0;
    }
  } else if (k2 == 1) {
    if (a01 + a10 == 0) {
      k2 = 0;
      for (int i = 1; i <= k1; i++) printf("0");
      return 0;
    }
  }
  if (a10 + a01 != k1 * k2) {
    cout << "Impossible\n";
    return 0;
  }
  long long m = a10 / k1, n = a10 % k1;
  k2 -= m;
  string s;
  for (int i = 0; i < m; i++) s += '1';
  for (int i = k1; i > 0; i--) {
    if (i == n) {
      s += '1';
      k2--;
    }
    s += '0';
  }
  for (int i = 0; i < k2; i++) s += '1';
  cout << s;
}

```