#include <bits/stdc++.h>
using namespace std;
int main() {
  int a00, a01, a10, a11;
  cin >> a00 >> a01 >> a10 >> a11;
  if (!a00 && !a01 && !a10 && !a11) {
    cout << '0';
    return 0;
  }
  int cnt0 = -1, cnt1 = -1;
  for (int i = 0; (i * (i - 1)) / 2 <= 1e9; ++i) {
    if (i * (i - 1) / 2 == a00) cnt0 = i;
    if (i * (i - 1) / 2 == a11) cnt1 = i;
  }
  if (cnt0 == -1 || cnt1 == -1) {
    cout << "Impossible";
    return 0;
  }
  if (!a01 && !a10 && !a11) {
    string s = "";
    for (int j = 0; j < cnt0; ++j) s += '0';
    cout << s;
    return 0;
  }
  if (!a01 && !a10 && !a00) {
    string s = "";
    for (int j = 0; j < cnt1; ++j) s += '1';
    cout << s;
    return 0;
  }
  if (cnt0 == -1 || cnt1 == -1 || cnt0 * cnt1 != a01 + a10) {
    cout << "Impossible";
    return 0;
  }
  string s = "";
  while (cnt0 + cnt1 != 0) {
    if (a01 >= cnt1) {
      cout << 0;
      a01 -= cnt1;
      --cnt0;
    } else {
      cout << 1;
      a10 -= cnt0;
      --cnt1;
    }
  }
}

### Prompt

Please provide a Cpp coded solution to the problem described below:

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() {
  int a00, a01, a10, a11;
  cin >> a00 >> a01 >> a10 >> a11;
  if (!a00 && !a01 && !a10 && !a11) {
    cout << '0';
    return 0;
  }
  int cnt0 = -1, cnt1 = -1;
  for (int i = 0; (i * (i - 1)) / 2 <= 1e9; ++i) {
    if (i * (i - 1) / 2 == a00) cnt0 = i;
    if (i * (i - 1) / 2 == a11) cnt1 = i;
  }
  if (cnt0 == -1 || cnt1 == -1) {
    cout << "Impossible";
    return 0;
  }
  if (!a01 && !a10 && !a11) {
    string s = "";
    for (int j = 0; j < cnt0; ++j) s += '0';
    cout << s;
    return 0;
  }
  if (!a01 && !a10 && !a00) {
    string s = "";
    for (int j = 0; j < cnt1; ++j) s += '1';
    cout << s;
    return 0;
  }
  if (cnt0 == -1 || cnt1 == -1 || cnt0 * cnt1 != a01 + a10) {
    cout << "Impossible";
    return 0;
  }
  string s = "";
  while (cnt0 + cnt1 != 0) {
    if (a01 >= cnt1) {
      cout << 0;
      a01 -= cnt1;
      --cnt0;
    } else {
      cout << 1;
      a10 -= cnt0;
      --cnt1;
    }
  }
}

```