#include <bits/stdc++.h>
using namespace std;
int a00, a01, a10, a11, n, m;
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cin >> a00 >> a01 >> a10 >> a11;
  for (int i = 1; i * (i - 1) <= 2 * max(a00, a11); i++) {
    if (i * (i - 1) == 2 * a00) m = i;
    if (i * (i - 1) == 2 * a11) n = i;
  }
  if (!a01 && !a10 && (!a00 || !a11)) {
    for (int i = 0; i < (a00 ? m : n); i++) cout << (a11 > 0);
    if (!(a00 ? m : n)) cout << "Impossible";
    cout << endl;
    return 0;
  }
  if (!n || !m || n * m != a01 + a10) {
    cout << "Impossible\n";
    return 0;
  }
  for (int i = 0; i < a10 / m; i++) cout << 1;
  for (int i = 0; i < m - a10 % m; i++) cout << 0;
  if (a10 % m) cout << 1;
  for (int i = m - a10 % m; i < m; i++) cout << 0;
  for (int i = a10 / m + (a10 % m > 0); i < n; i++) cout << 1;
  cout << endl;
  return 0;
}

### Prompt

Please formulate 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 a00, a01, a10, a11, n, m;
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cin >> a00 >> a01 >> a10 >> a11;
  for (int i = 1; i * (i - 1) <= 2 * max(a00, a11); i++) {
    if (i * (i - 1) == 2 * a00) m = i;
    if (i * (i - 1) == 2 * a11) n = i;
  }
  if (!a01 && !a10 && (!a00 || !a11)) {
    for (int i = 0; i < (a00 ? m : n); i++) cout << (a11 > 0);
    if (!(a00 ? m : n)) cout << "Impossible";
    cout << endl;
    return 0;
  }
  if (!n || !m || n * m != a01 + a10) {
    cout << "Impossible\n";
    return 0;
  }
  for (int i = 0; i < a10 / m; i++) cout << 1;
  for (int i = 0; i < m - a10 % m; i++) cout << 0;
  if (a10 % m) cout << 1;
  for (int i = m - a10 % m; i < m; i++) cout << 0;
  for (int i = a10 / m + (a10 % m > 0); i < n; i++) cout << 1;
  cout << endl;
  return 0;
}

```