#include <bits/stdc++.h>
using namespace std;
string s;
int check(long long a) {
  for (int i = 1; i <= 1000000; ++i) {
    long long x = 1ll * i * (i - 1) / 2;
    if (x == a) return i;
  }
  return -1;
}
int main() {
  srand(time(NULL));
  long long a, b, c, d;
  cin >> a >> b >> c >> d;
  int n = check(a);
  int m = check(d);
  if (n == -1 || m == -1) {
    cout << "Impossible" << endl;
    return 0;
  }
  if (a == 0 && b == 0 && c == 0 && d == 0) {
    cout << "0" << endl;
    return 0;
  }
  if (n == 1 && b == 0 && c == 0) {
    n = 0;
  }
  if (m == 1 && b == 0 && c == 0) {
    m = 0;
  }
  int dx = n + m;
  for (int i = 0; i < dx; ++i) {
    if (b - m >= 0) {
      b -= m;
      n -= 1;
      s += '0';
    } else if (c - n >= 0) {
      c -= n;
      m -= 1;
      s += '1';
    }
  }
  if (b == 0 && c == 0 && s.length() == dx) {
    cout << s << endl;
  } else {
    cout << "Impossible" << endl;
  }
}

### 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;
string s;
int check(long long a) {
  for (int i = 1; i <= 1000000; ++i) {
    long long x = 1ll * i * (i - 1) / 2;
    if (x == a) return i;
  }
  return -1;
}
int main() {
  srand(time(NULL));
  long long a, b, c, d;
  cin >> a >> b >> c >> d;
  int n = check(a);
  int m = check(d);
  if (n == -1 || m == -1) {
    cout << "Impossible" << endl;
    return 0;
  }
  if (a == 0 && b == 0 && c == 0 && d == 0) {
    cout << "0" << endl;
    return 0;
  }
  if (n == 1 && b == 0 && c == 0) {
    n = 0;
  }
  if (m == 1 && b == 0 && c == 0) {
    m = 0;
  }
  int dx = n + m;
  for (int i = 0; i < dx; ++i) {
    if (b - m >= 0) {
      b -= m;
      n -= 1;
      s += '0';
    } else if (c - n >= 0) {
      c -= n;
      m -= 1;
      s += '1';
    }
  }
  if (b == 0 && c == 0 && s.length() == dx) {
    cout << s << endl;
  } else {
    cout << "Impossible" << endl;
  }
}

```