#include <bits/stdc++.h>
using namespace std;
long long a, b, c, d, x, y;
long long findnot(long long result) {
  if (result == 0) return 1;
  for (int i = 0; i * i <= result; i++) {
    if (i * (i + 1) == result) {
      return i + 1;
    }
  }
  return -1;
}
int main() {
  cin >> a >> b >> c >> d;
  a *= 2;
  d *= 2;
  x = findnot(a);
  y = findnot(d);
  if (a == 0 && d == 0 && b == 0 && c == 0) cout << "1" << endl, exit(0);
  if (a == 0 && b == 0 && c == 0) x = 0;
  if (d == 0 && c == 0 && b == 0) y = 0;
  if (x == -1 || y == -1 || (x * y) != b + c) {
    cout << "Impossible" << endl;
    exit(0);
  }
  long long z = 0;
  if (x)
    for (long long i = 0; i < (x * y - b) / x; i++) cout << "1", z++;
  if (x)
    for (long long i = 0; i < (x - ((x * y - b) % x)); i++) cout << "0";
  if (x)
    if ((x * y - b) % x != 0) cout << "1", z++;
  if (x)
    for (long long i = 0; i < (x * y - b) % x; i++) cout << "0";
  for (long long i = 0; i < (y - z); i++) cout << "1";
  cout << endl;
}

### Prompt

Your challenge is to write 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 a, b, c, d, x, y;
long long findnot(long long result) {
  if (result == 0) return 1;
  for (int i = 0; i * i <= result; i++) {
    if (i * (i + 1) == result) {
      return i + 1;
    }
  }
  return -1;
}
int main() {
  cin >> a >> b >> c >> d;
  a *= 2;
  d *= 2;
  x = findnot(a);
  y = findnot(d);
  if (a == 0 && d == 0 && b == 0 && c == 0) cout << "1" << endl, exit(0);
  if (a == 0 && b == 0 && c == 0) x = 0;
  if (d == 0 && c == 0 && b == 0) y = 0;
  if (x == -1 || y == -1 || (x * y) != b + c) {
    cout << "Impossible" << endl;
    exit(0);
  }
  long long z = 0;
  if (x)
    for (long long i = 0; i < (x * y - b) / x; i++) cout << "1", z++;
  if (x)
    for (long long i = 0; i < (x - ((x * y - b) % x)); i++) cout << "0";
  if (x)
    if ((x * y - b) % x != 0) cout << "1", z++;
  if (x)
    for (long long i = 0; i < (x * y - b) % x; i++) cout << "0";
  for (long long i = 0; i < (y - z); i++) cout << "1";
  cout << endl;
}

```