#include <bits/stdc++.h>
using namespace std;
long long int func(long long int num) {
  long long int i = 1;
  while (i * (i - 1) <= 2 * num) {
    if (i * (i - 1) == 2 * num) {
      return i;
    }
    i++;
  }
  return -1;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  long long int arr[4];
  long long int sum = 0;
  for (int i = 0; i < 4; i++) {
    cin >> arr[i];
    sum += arr[i];
  }
  long long int x, y;
  x = func(arr[0]);
  y = func(arr[3]);
  if (x == -1 or y == -1) {
    cout << "Impossible\n";
    return 0;
  }
  if (sum == 0) {
    cout << "0\n";
    return 0;
  }
  if (sum == 1) {
    if (arr[0] == 1) {
      cout << "00\n";
    } else if (arr[1] == 1) {
      cout << "01\n";
    } else if (arr[2] == 1) {
      cout << "10\n";
    } else {
      cout << "11\n";
    }
    return 0;
  }
  if (arr[0] == 0) {
    if (arr[1] + arr[2] == 0) {
      x = 0;
    }
  }
  if (arr[3] == 0) {
    if (arr[1] + arr[2] == 0) {
      y = 0;
    }
  }
  if (x * y != arr[1] + arr[2]) {
    cout << "Impossible\n";
    return 0;
  }
  while (x + y > 0) {
    if (arr[1] >= y) {
      cout << "0";
      arr[1] -= y;
      x--;
    } else {
      cout << "1";
      arr[2] -= x;
      y--;
    }
  }
  cout << "\n";
  return 0;
}

### Prompt

Construct a cpp code solution to the problem outlined:

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 int func(long long int num) {
  long long int i = 1;
  while (i * (i - 1) <= 2 * num) {
    if (i * (i - 1) == 2 * num) {
      return i;
    }
    i++;
  }
  return -1;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  long long int arr[4];
  long long int sum = 0;
  for (int i = 0; i < 4; i++) {
    cin >> arr[i];
    sum += arr[i];
  }
  long long int x, y;
  x = func(arr[0]);
  y = func(arr[3]);
  if (x == -1 or y == -1) {
    cout << "Impossible\n";
    return 0;
  }
  if (sum == 0) {
    cout << "0\n";
    return 0;
  }
  if (sum == 1) {
    if (arr[0] == 1) {
      cout << "00\n";
    } else if (arr[1] == 1) {
      cout << "01\n";
    } else if (arr[2] == 1) {
      cout << "10\n";
    } else {
      cout << "11\n";
    }
    return 0;
  }
  if (arr[0] == 0) {
    if (arr[1] + arr[2] == 0) {
      x = 0;
    }
  }
  if (arr[3] == 0) {
    if (arr[1] + arr[2] == 0) {
      y = 0;
    }
  }
  if (x * y != arr[1] + arr[2]) {
    cout << "Impossible\n";
    return 0;
  }
  while (x + y > 0) {
    if (arr[1] >= y) {
      cout << "0";
      arr[1] -= y;
      x--;
    } else {
      cout << "1";
      arr[2] -= x;
      y--;
    }
  }
  cout << "\n";
  return 0;
}

```