#include <bits/stdc++.h>
using namespace std;
long long calc(long long n) {
  long long i = 1;
  while (i * (i - 1) / 2 < n) {
    i++;
  }
  if (i * (i - 1) / 2 == n) {
    return i;
  }
  return -1;
}
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  long long a00, a01, a10, a11;
  cin >> a00 >> a01 >> a10 >> a11;
  long long n = calc(a00 + a01 + a10 + a11);
  if (a00 + a01 + a10 + a11 == 0) {
    cout << "0\n";
  } else if (n == -1) {
    cout << "Impossible\n";
  } else if (a00 == 0 && a01 == 0 && a10 == 0) {
    cout << string(n, '1') << '\n';
  } else if (a11 == 0 && a01 == 0 && a10 == 0) {
    cout << string(n, '0') << '\n';
  } else {
    long long n0 = calc(a00);
    long long n1 = calc(a11);
    if (n0 == -1 || n1 == -1 || n0 + n1 != n) {
      cout << "Impossible\n";
    } else if (a10 == 0) {
      cout << string(n0, '0') + string(n1, '1') << '\n';
    } else {
      cout << string(n0 - (a10 + n1 - 1) / n1, '0') +
                  string(a10 % n1 == 0 ? n1 : a10 % n1, '1') + "0" +
                  string(n1 - (a10 % n1 == 0 ? n1 : a10 % n1), '1') +
                  string((a10 + n1 - 1) / n1 - 1, '0')
           << '\n';
    }
  }
  return 0;
}

### Prompt

Please create a solution in cpp 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;
long long calc(long long n) {
  long long i = 1;
  while (i * (i - 1) / 2 < n) {
    i++;
  }
  if (i * (i - 1) / 2 == n) {
    return i;
  }
  return -1;
}
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  long long a00, a01, a10, a11;
  cin >> a00 >> a01 >> a10 >> a11;
  long long n = calc(a00 + a01 + a10 + a11);
  if (a00 + a01 + a10 + a11 == 0) {
    cout << "0\n";
  } else if (n == -1) {
    cout << "Impossible\n";
  } else if (a00 == 0 && a01 == 0 && a10 == 0) {
    cout << string(n, '1') << '\n';
  } else if (a11 == 0 && a01 == 0 && a10 == 0) {
    cout << string(n, '0') << '\n';
  } else {
    long long n0 = calc(a00);
    long long n1 = calc(a11);
    if (n0 == -1 || n1 == -1 || n0 + n1 != n) {
      cout << "Impossible\n";
    } else if (a10 == 0) {
      cout << string(n0, '0') + string(n1, '1') << '\n';
    } else {
      cout << string(n0 - (a10 + n1 - 1) / n1, '0') +
                  string(a10 % n1 == 0 ? n1 : a10 % n1, '1') + "0" +
                  string(n1 - (a10 % n1 == 0 ? n1 : a10 % n1), '1') +
                  string((a10 + n1 - 1) / n1 - 1, '0')
           << '\n';
    }
  }
  return 0;
}

```