#include <bits/stdc++.h>
using namespace std;
long long trans(long long x) {
  x *= 2;
  long long i = 0, j = 100000, tmp = 0;
  while (i <= j) {
    long long mid = (i + j) / 2;
    if (mid * mid <= x) {
      tmp = mid;
      i = mid + 1;
    } else
      j = mid - 1;
  }
  if (x != tmp * (tmp + 1))
    return -1;
  else
    return (tmp + 1);
}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  long long a00, a01, a10, a11;
  long long n0, n1, nt;
  cin >> a00 >> a01 >> a10 >> a11;
  if ((a00 + a01 + a10) == 0)
    n0 = 0;
  else
    n0 = trans(a00);
  if ((a11 + a01 + a10) == 0)
    n1 = 0;
  else
    n1 = trans(a11);
  nt = trans(a00 + a01 + a11 + a10);
  if ((a00 + a01 + a11 + a10) == 0)
    cout << 0;
  else if (n0 == -1 || n1 == -1 || nt == -1 || nt != (n1 + n0) || nt == 0)
    cout << "Impossible";
  else {
    for (int i = 0; i < nt; i++) {
      if (a10 >= n0) {
        cout << 1;
        a10 -= n0;
        n1--;
      } else {
        cout << 0;
        a01 -= n1;
        n0--;
      }
    }
  }
}

### 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 trans(long long x) {
  x *= 2;
  long long i = 0, j = 100000, tmp = 0;
  while (i <= j) {
    long long mid = (i + j) / 2;
    if (mid * mid <= x) {
      tmp = mid;
      i = mid + 1;
    } else
      j = mid - 1;
  }
  if (x != tmp * (tmp + 1))
    return -1;
  else
    return (tmp + 1);
}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  long long a00, a01, a10, a11;
  long long n0, n1, nt;
  cin >> a00 >> a01 >> a10 >> a11;
  if ((a00 + a01 + a10) == 0)
    n0 = 0;
  else
    n0 = trans(a00);
  if ((a11 + a01 + a10) == 0)
    n1 = 0;
  else
    n1 = trans(a11);
  nt = trans(a00 + a01 + a11 + a10);
  if ((a00 + a01 + a11 + a10) == 0)
    cout << 0;
  else if (n0 == -1 || n1 == -1 || nt == -1 || nt != (n1 + n0) || nt == 0)
    cout << "Impossible";
  else {
    for (int i = 0; i < nt; i++) {
      if (a10 >= n0) {
        cout << 1;
        a10 -= n0;
        n1--;
      } else {
        cout << 0;
        a01 -= n1;
        n0--;
      }
    }
  }
}

```