#include <bits/stdc++.h>
using namespace std;
long long a, b, c, d, n, m, cnt, len;
int main() {
  cin >> a >> b >> c >> d;
  if (a + b + c + d == 0) {
    cout << 0;
    return 0;
  }
  if (a > 0 && b + c + d == 0) {
    a *= 2;
    n = sqrt(1 + 4 * a);
    if (n * n != 1 + 4 * a || (1 + n) % 2) {
      cout << "Impossible";
      return 0;
    }
    n = (1 + n) / 2;
    for (int i = 0; i < n; i++) printf("0");
    return 0;
  }
  if (d > 0 && b + c + a == 0) {
    d *= 2;
    m = sqrt(1 + 4 * d);
    if (m * m != 1 + 4 * d || (1 + m) % 2) {
      cout << "Impossible";
      return 0;
    }
    m = (1 + m) / 2;
    for (int i = 0; i < m; i++) printf("1");
    return 0;
  }
  a *= 2;
  n = sqrt(1 + 4 * a);
  if (n * n != 1 + 4 * a || (1 + n) % 2) {
    cout << "Impossible";
    return 0;
  }
  n = (1 + n) / 2;
  d *= 2;
  m = sqrt(1 + 4 * d);
  if (m * m != 1 + 4 * d || (1 + m) % 2) {
    cout << "Impossible";
    return 0;
  }
  m = (1 + m) / 2;
  if (n == 0 && m == 0) n = m = 1;
  cnt = n * m;
  if (cnt != b + c) {
    cout << "Impossible";
    return 0;
  }
  len = n + m;
  for (int i = 0; i < len; i++) {
    if (b >= m) {
      b -= m;
      n--;
      printf("0");
    } else {
      c -= n;
      m--;
      printf("1");
    }
  }
  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;
long long a, b, c, d, n, m, cnt, len;
int main() {
  cin >> a >> b >> c >> d;
  if (a + b + c + d == 0) {
    cout << 0;
    return 0;
  }
  if (a > 0 && b + c + d == 0) {
    a *= 2;
    n = sqrt(1 + 4 * a);
    if (n * n != 1 + 4 * a || (1 + n) % 2) {
      cout << "Impossible";
      return 0;
    }
    n = (1 + n) / 2;
    for (int i = 0; i < n; i++) printf("0");
    return 0;
  }
  if (d > 0 && b + c + a == 0) {
    d *= 2;
    m = sqrt(1 + 4 * d);
    if (m * m != 1 + 4 * d || (1 + m) % 2) {
      cout << "Impossible";
      return 0;
    }
    m = (1 + m) / 2;
    for (int i = 0; i < m; i++) printf("1");
    return 0;
  }
  a *= 2;
  n = sqrt(1 + 4 * a);
  if (n * n != 1 + 4 * a || (1 + n) % 2) {
    cout << "Impossible";
    return 0;
  }
  n = (1 + n) / 2;
  d *= 2;
  m = sqrt(1 + 4 * d);
  if (m * m != 1 + 4 * d || (1 + m) % 2) {
    cout << "Impossible";
    return 0;
  }
  m = (1 + m) / 2;
  if (n == 0 && m == 0) n = m = 1;
  cnt = n * m;
  if (cnt != b + c) {
    cout << "Impossible";
    return 0;
  }
  len = n + m;
  for (int i = 0; i < len; i++) {
    if (b >= m) {
      b -= m;
      n--;
      printf("0");
    } else {
      c -= n;
      m--;
      printf("1");
    }
  }
  return 0;
}

```