#include <bits/stdc++.h>
using namespace std;
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  long long a, b, c, d;
  cin >> a >> b >> c >> d;
  if (a == 0) {
    if (b == 0 && c == 0) {
      long long ones = (long long)sqrt(2 * d);
      if (d != ((ones) * (ones + 1)) / 2) {
        cout << "Impossible";
        return 0;
      } else {
        for (int i = 0; i < ones + 1; i++) {
          cout << "1";
        }
        return 0;
      }
    }
    if (b > 100000 || c > 100000 ||
        (b * (b - 1)) / 2 + (c * (c - 1)) / 2 + b * c != d) {
      cout << "Impossible";
      return 0;
    }
    for (int i = 0; i < c; i++) {
      cout << "1";
    }
    cout << "0";
    for (int i = 0; i < b; i++) {
      cout << "1";
    }
    return 0;
  }
  if (d == 0) {
    if (b == 0 && c == 0) {
      long long ones = (long long)sqrt(2 * a);
      if (a != ((ones) * (ones + 1)) / 2) {
        cout << "Impossible";
        return 0;
      } else {
        for (int i = 0; i < ones + 1; i++) {
          cout << "0";
        }
        return 0;
      }
    }
    if (b > 100000 || c > 100000 ||
        (b * (b - 1)) / 2 + (c * (c - 1)) / 2 + b * c != a) {
      cout << "Impossible";
      return 0;
    }
    for (int i = 0; i < b; i++) {
      cout << "0";
    }
    cout << "1";
    for (int i = 0; i < c; i++) {
      cout << "0";
    }
    return 0;
  }
  long long zeros = (long long)sqrt(2 * a);
  long long ones = (long long)sqrt(2 * d);
  if (a != ((zeros) * (zeros + 1)) / 2 || d != ((ones) * (ones + 1)) / 2) {
    cout << "Impossible";
    return 0;
  }
  zeros++;
  ones++;
  if (zeros * ones != b + c) {
    cout << "Impossible";
    return 0;
  }
  long long zeroOne = ones * zeros;
  long long num = c / zeros;
  long long rem = c % zeros;
  for (long long i = 0; i < num; i++) {
    cout << "1";
  }
  for (long long i = 0; i < zeros - rem; i++) {
    cout << "0";
  }
  if (num != ones) cout << "1";
  for (long long i = 0; i < rem; i++) {
    cout << "0";
  }
  for (long long i = 0; i < ones - num - 1; i++) {
    cout << "1";
  }
  return 0;
}

### Prompt

Your task is to create 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() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  long long a, b, c, d;
  cin >> a >> b >> c >> d;
  if (a == 0) {
    if (b == 0 && c == 0) {
      long long ones = (long long)sqrt(2 * d);
      if (d != ((ones) * (ones + 1)) / 2) {
        cout << "Impossible";
        return 0;
      } else {
        for (int i = 0; i < ones + 1; i++) {
          cout << "1";
        }
        return 0;
      }
    }
    if (b > 100000 || c > 100000 ||
        (b * (b - 1)) / 2 + (c * (c - 1)) / 2 + b * c != d) {
      cout << "Impossible";
      return 0;
    }
    for (int i = 0; i < c; i++) {
      cout << "1";
    }
    cout << "0";
    for (int i = 0; i < b; i++) {
      cout << "1";
    }
    return 0;
  }
  if (d == 0) {
    if (b == 0 && c == 0) {
      long long ones = (long long)sqrt(2 * a);
      if (a != ((ones) * (ones + 1)) / 2) {
        cout << "Impossible";
        return 0;
      } else {
        for (int i = 0; i < ones + 1; i++) {
          cout << "0";
        }
        return 0;
      }
    }
    if (b > 100000 || c > 100000 ||
        (b * (b - 1)) / 2 + (c * (c - 1)) / 2 + b * c != a) {
      cout << "Impossible";
      return 0;
    }
    for (int i = 0; i < b; i++) {
      cout << "0";
    }
    cout << "1";
    for (int i = 0; i < c; i++) {
      cout << "0";
    }
    return 0;
  }
  long long zeros = (long long)sqrt(2 * a);
  long long ones = (long long)sqrt(2 * d);
  if (a != ((zeros) * (zeros + 1)) / 2 || d != ((ones) * (ones + 1)) / 2) {
    cout << "Impossible";
    return 0;
  }
  zeros++;
  ones++;
  if (zeros * ones != b + c) {
    cout << "Impossible";
    return 0;
  }
  long long zeroOne = ones * zeros;
  long long num = c / zeros;
  long long rem = c % zeros;
  for (long long i = 0; i < num; i++) {
    cout << "1";
  }
  for (long long i = 0; i < zeros - rem; i++) {
    cout << "0";
  }
  if (num != ones) cout << "1";
  for (long long i = 0; i < rem; i++) {
    cout << "0";
  }
  for (long long i = 0; i < ones - num - 1; i++) {
    cout << "1";
  }
  return 0;
}

```