#include <bits/stdc++.h>
using namespace std;
long long int gcd(long long int a, long long int b) {
  if (a % b == 0) {
    return b;
  } else {
    return gcd(b, a % b);
  }
}
void imp() {
  cout << "Impossible\n";
  exit(0);
}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(NULL);
  cout.tie(NULL);
  long long int a00, a01, a10, a11, c0, c1, x;
  cin >> a00 >> a01 >> a10 >> a11;
  c0 = sqrtl(2 * a00) + 1;
  c1 = sqrtl(2 * a11) + 1;
  if (a00 == 0 || a11 == 0) {
    if (a01 == 0 && a10 == 0) {
      if (a00 == 0) {
        c0 = 0;
      }
      if (a11 == 0) {
        c1 = 0;
      }
    }
  }
  if (c0 == 0 && c1 == 0) {
    cout << 0 << "\n";
    exit(0);
  } else if ((c0 * (c0 - 1)) / 2 != a00) {
    imp();
  } else if ((c1 * (c1 - 1)) / 2 != a11) {
    imp();
  }
  if (c0 * c1 != a01 + a10) {
    imp();
  }
  x = c0 + c1;
  for (int i = 1; i < x + 1; i++) {
    if (a01 >= c1) {
      cout << 0;
      a01 -= c1;
      c0--;
    } else {
      cout << 1;
      a10 -= c0;
      c1--;
    }
  }
  cout << "\n";
  return 0;
}

### Prompt

Generate 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;
long long int gcd(long long int a, long long int b) {
  if (a % b == 0) {
    return b;
  } else {
    return gcd(b, a % b);
  }
}
void imp() {
  cout << "Impossible\n";
  exit(0);
}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(NULL);
  cout.tie(NULL);
  long long int a00, a01, a10, a11, c0, c1, x;
  cin >> a00 >> a01 >> a10 >> a11;
  c0 = sqrtl(2 * a00) + 1;
  c1 = sqrtl(2 * a11) + 1;
  if (a00 == 0 || a11 == 0) {
    if (a01 == 0 && a10 == 0) {
      if (a00 == 0) {
        c0 = 0;
      }
      if (a11 == 0) {
        c1 = 0;
      }
    }
  }
  if (c0 == 0 && c1 == 0) {
    cout << 0 << "\n";
    exit(0);
  } else if ((c0 * (c0 - 1)) / 2 != a00) {
    imp();
  } else if ((c1 * (c1 - 1)) / 2 != a11) {
    imp();
  }
  if (c0 * c1 != a01 + a10) {
    imp();
  }
  x = c0 + c1;
  for (int i = 1; i < x + 1; i++) {
    if (a01 >= c1) {
      cout << 0;
      a01 -= c1;
      c0--;
    } else {
      cout << 1;
      a10 -= c0;
      c1--;
    }
  }
  cout << "\n";
  return 0;
}

```