#include <bits/stdc++.h>
using namespace std;
string s;
int a00, a01, a10, a11, n, m, cnt1, cnt0;
int bfzero = 0;
int f(long long x) {
  int d = sqrt(8 * x + 1);
  int n0 = (-1 + d) / 2;
  return n0;
}
void build(int a00, int a01, int a10, int a11) {
  n = f(a00) + 1;
  m = f(a11) + 1;
  if (n * (n - 1) / 2 != a00 || (m * (m - 1) / 2 != a11)) {
    cout << "Impossible";
    return;
  }
  if (a01 == 0 and a10 == 0) {
    if (a00 == 0) {
      for (int i = 0; i < m; i++) {
        cout << '1';
      }
      cout << endl;
      return;
    } else if (a11 == 0) {
      for (int i = 0; i < n; i++) {
        cout << '0';
      }
      cout << endl;
      return;
    }
  }
  if (n * m != (a01 + a10)) {
    cout << "Impossible";
    return;
  }
  int cnt1 = m, cnt0 = n;
  for (int i = 0; i <= cnt0; i++) {
    while (a10 >= cnt0 - i && a01 >= i) {
      cout << 1;
      a10 -= cnt0 - i;
      a01 -= i;
    }
    if (i != cnt0) {
      cout << 0;
    }
  }
}
int main() {
  cin >> a00 >> a01 >> a10 >> a11;
  build(a00, a01, a10, a11);
  return 0;
}

### 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 a00, a01, a10, a11, n, m, cnt1, cnt0;
int bfzero = 0;
int f(long long x) {
  int d = sqrt(8 * x + 1);
  int n0 = (-1 + d) / 2;
  return n0;
}
void build(int a00, int a01, int a10, int a11) {
  n = f(a00) + 1;
  m = f(a11) + 1;
  if (n * (n - 1) / 2 != a00 || (m * (m - 1) / 2 != a11)) {
    cout << "Impossible";
    return;
  }
  if (a01 == 0 and a10 == 0) {
    if (a00 == 0) {
      for (int i = 0; i < m; i++) {
        cout << '1';
      }
      cout << endl;
      return;
    } else if (a11 == 0) {
      for (int i = 0; i < n; i++) {
        cout << '0';
      }
      cout << endl;
      return;
    }
  }
  if (n * m != (a01 + a10)) {
    cout << "Impossible";
    return;
  }
  int cnt1 = m, cnt0 = n;
  for (int i = 0; i <= cnt0; i++) {
    while (a10 >= cnt0 - i && a01 >= i) {
      cout << 1;
      a10 -= cnt0 - i;
      a01 -= i;
    }
    if (i != cnt0) {
      cout << 0;
    }
  }
}
int main() {
  cin >> a00 >> a01 >> a10 >> a11;
  build(a00, a01, a10, a11);
  return 0;
}

```