#include <bits/stdc++.h>
using namespace std;
vector<int> ans;
long long zz, zj, jz, jj, len = -1, sum, lz = -1, lj = -1;
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cin >> zz >> zj >> jz >> jj;
  long long sum = zz + zj + jz + jj;
  if (sum == 0) {
    cout << 0;
    return 0;
  }
  for (long long a = 1; a <= 300000; a++) {
    if (((a * (a - 1)) / 2) == sum) {
      len = a;
      break;
    }
  }
  if (len == -1) {
    cout << "Impossible";
    return 0;
  }
  long long n = len;
  for (long long a = 1; a <= 300000; a++) {
    if (((a * (a - 1)) / 2) == zz) {
      lz = a;
      break;
    }
  }
  if (lz == -1) {
    cout << "Impossible";
    return 0;
  }
  for (long long a = 1; a <= 300000; a++) {
    if (((a * (a - 1)) / 2) == jj) {
      lj = a;
      break;
    }
  }
  if (jj + jz + zj == 0) lj = 0;
  if (zz + jz + zj == 0) lz = 0;
  if (lj == -1) {
    cout << "Impossible";
    return 0;
  }
  if (lz == 0) {
    for (int a = 0; a < lj; a++) cout << "1";
    return 0;
  }
  if (lj == 0) {
    for (int a = 1; a <= lz; a++) cout << "0";
    return 0;
  }
  if (jz + zj != lz * lj) {
    cout << "Impossible";
    return 0;
  } else {
    for (int a = 1; a <= lz; a++) {
      if (jz > 0) {
        if (lj <= jz) {
          jz -= lj;
          ans.push_back(lj + 1);
        } else {
          ans.push_back(lj + 1 - (lj - jz));
          jz = 0;
        }
      } else {
        ans.push_back(1);
      }
    }
    sort(ans.begin(), ans.end());
    int pos = 1;
    for (int a = 0; a < ans.size();) {
      if (ans[a] > pos) {
        cout << "1";
        pos++;
      } else {
        cout << "0";
        a++;
      }
    }
    while (pos <= lj) {
      cout << "1";
      pos++;
    }
    return 0;
  }
  return 0;
}

### Prompt

Develop a solution in cpp 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;
vector<int> ans;
long long zz, zj, jz, jj, len = -1, sum, lz = -1, lj = -1;
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cin >> zz >> zj >> jz >> jj;
  long long sum = zz + zj + jz + jj;
  if (sum == 0) {
    cout << 0;
    return 0;
  }
  for (long long a = 1; a <= 300000; a++) {
    if (((a * (a - 1)) / 2) == sum) {
      len = a;
      break;
    }
  }
  if (len == -1) {
    cout << "Impossible";
    return 0;
  }
  long long n = len;
  for (long long a = 1; a <= 300000; a++) {
    if (((a * (a - 1)) / 2) == zz) {
      lz = a;
      break;
    }
  }
  if (lz == -1) {
    cout << "Impossible";
    return 0;
  }
  for (long long a = 1; a <= 300000; a++) {
    if (((a * (a - 1)) / 2) == jj) {
      lj = a;
      break;
    }
  }
  if (jj + jz + zj == 0) lj = 0;
  if (zz + jz + zj == 0) lz = 0;
  if (lj == -1) {
    cout << "Impossible";
    return 0;
  }
  if (lz == 0) {
    for (int a = 0; a < lj; a++) cout << "1";
    return 0;
  }
  if (lj == 0) {
    for (int a = 1; a <= lz; a++) cout << "0";
    return 0;
  }
  if (jz + zj != lz * lj) {
    cout << "Impossible";
    return 0;
  } else {
    for (int a = 1; a <= lz; a++) {
      if (jz > 0) {
        if (lj <= jz) {
          jz -= lj;
          ans.push_back(lj + 1);
        } else {
          ans.push_back(lj + 1 - (lj - jz));
          jz = 0;
        }
      } else {
        ans.push_back(1);
      }
    }
    sort(ans.begin(), ans.end());
    int pos = 1;
    for (int a = 0; a < ans.size();) {
      if (ans[a] > pos) {
        cout << "1";
        pos++;
      } else {
        cout << "0";
        a++;
      }
    }
    while (pos <= lj) {
      cout << "1";
      pos++;
    }
    return 0;
  }
  return 0;
}

```