#include <bits/stdc++.h>
using namespace std;
signed main() {
  long long z, o, zo, oz;
  cin >> z >> zo >> oz >> o;
  if (z == 0 && oz == 0 && zo == 0 && o == 0) {
    cout << "0";
    return 0;
  }
  if (z == 0 && o == 0 && zo == 1 && oz == 0) {
    cout << "01";
    return 0;
  }
  if (z == 0 && o == 0 && zo == 0 && oz == 1) {
    cout << "10";
    return 0;
  }
  long long nz, no;
  nz = no = -1;
  for (long long i = 0; i <= 1e5; i++) {
    if (i * (i - 1) / 2 == z) {
      nz = i;
    }
    if (i * (i - 1) / 2 == o) {
      no = i;
    }
  }
  if (oz == 0 && zo == 0 && o && z == 0) nz = 0;
  if (oz == 0 && zo == 0 && z && o == 0) no = 0;
  if (nz == -1 || no == -1) {
    cout << "Impossible";
    return 0;
  }
  if (nz * no != oz + zo) {
    cout << "Impossible";
    return 0;
  }
  deque<char> a;
  for (long long i = 0; i < nz; i++) a.push_back('0');
  while (no--) {
    if (zo >= nz) {
      a.push_back('1');
      zo -= nz;
    } else if (zo) {
      auto it = a.begin() + zo;
      a.insert(it, '1');
      zo = 0;
    } else if (zo == 0) {
      a.push_front('1');
    }
  }
  for (char x : a) cout << x;
  return 0;
}

### Prompt

Create a solution in Cpp for 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;
signed main() {
  long long z, o, zo, oz;
  cin >> z >> zo >> oz >> o;
  if (z == 0 && oz == 0 && zo == 0 && o == 0) {
    cout << "0";
    return 0;
  }
  if (z == 0 && o == 0 && zo == 1 && oz == 0) {
    cout << "01";
    return 0;
  }
  if (z == 0 && o == 0 && zo == 0 && oz == 1) {
    cout << "10";
    return 0;
  }
  long long nz, no;
  nz = no = -1;
  for (long long i = 0; i <= 1e5; i++) {
    if (i * (i - 1) / 2 == z) {
      nz = i;
    }
    if (i * (i - 1) / 2 == o) {
      no = i;
    }
  }
  if (oz == 0 && zo == 0 && o && z == 0) nz = 0;
  if (oz == 0 && zo == 0 && z && o == 0) no = 0;
  if (nz == -1 || no == -1) {
    cout << "Impossible";
    return 0;
  }
  if (nz * no != oz + zo) {
    cout << "Impossible";
    return 0;
  }
  deque<char> a;
  for (long long i = 0; i < nz; i++) a.push_back('0');
  while (no--) {
    if (zo >= nz) {
      a.push_back('1');
      zo -= nz;
    } else if (zo) {
      auto it = a.begin() + zo;
      a.insert(it, '1');
      zo = 0;
    } else if (zo == 0) {
      a.push_front('1');
    }
  }
  for (char x : a) cout << x;
  return 0;
}

```