#include <bits/stdc++.h>
using namespace std;
int main() {
  int a[2][2];
  cin >> a[0][0] >> a[0][1] >> a[1][0] >> a[1][1];
  int n[2];
  if (!a[0][0] && !a[1][0] && !a[0][1] && !a[1][1]) {
    cout << "0";
    return 0;
  }
  for (int i = 0; 1; i++) {
    int temp = i * (i - 1) / 2;
    if (temp == a[0][0]) {
      n[0] = i;
      break;
    }
    if (temp > a[0][0]) {
      cout << "Impossible";
      return 0;
    }
  }
  for (int i = 0; 1; i++) {
    int temp = i * (i - 1) / 2;
    if (temp == a[1][1]) {
      n[1] = i;
      break;
    }
    if (temp > a[1][1]) {
      cout << "Impossible";
      return 0;
    }
  }
  if (n[0] == 0)
    if (a[0][1] || a[1][0]) n[0] = 1;
  if (n[1] == 0)
    if (a[0][1] || a[1][0]) n[1] = 1;
  if ((a[0][1] + a[1][0]) != n[0] * n[1]) {
    cout << "Impossible";
    return 0;
  }
  int base = n[1];
  while (1) {
    if (a[0][1] > base) {
      cout << "0";
      n[0]--;
      a[0][1] -= base;
    } else {
      for (int i = 0; i < base - a[0][1]; ++i) cout << "1";
      if (n[0] > 0) {
        cout << "0";
        n[0]--;
      }
      for (int i = 0; i < a[0][1]; ++i) cout << "1";
      for (int i = 0; i < n[0]; ++i) cout << "0";
      break;
    }
  }
  return 0;
}

### Prompt

Your task is to create 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 main() {
  int a[2][2];
  cin >> a[0][0] >> a[0][1] >> a[1][0] >> a[1][1];
  int n[2];
  if (!a[0][0] && !a[1][0] && !a[0][1] && !a[1][1]) {
    cout << "0";
    return 0;
  }
  for (int i = 0; 1; i++) {
    int temp = i * (i - 1) / 2;
    if (temp == a[0][0]) {
      n[0] = i;
      break;
    }
    if (temp > a[0][0]) {
      cout << "Impossible";
      return 0;
    }
  }
  for (int i = 0; 1; i++) {
    int temp = i * (i - 1) / 2;
    if (temp == a[1][1]) {
      n[1] = i;
      break;
    }
    if (temp > a[1][1]) {
      cout << "Impossible";
      return 0;
    }
  }
  if (n[0] == 0)
    if (a[0][1] || a[1][0]) n[0] = 1;
  if (n[1] == 0)
    if (a[0][1] || a[1][0]) n[1] = 1;
  if ((a[0][1] + a[1][0]) != n[0] * n[1]) {
    cout << "Impossible";
    return 0;
  }
  int base = n[1];
  while (1) {
    if (a[0][1] > base) {
      cout << "0";
      n[0]--;
      a[0][1] -= base;
    } else {
      for (int i = 0; i < base - a[0][1]; ++i) cout << "1";
      if (n[0] > 0) {
        cout << "0";
        n[0]--;
      }
      for (int i = 0; i < a[0][1]; ++i) cout << "1";
      for (int i = 0; i < n[0]; ++i) cout << "0";
      break;
    }
  }
  return 0;
}

```