#include <bits/stdc++.h>
#pragma GCC optimise("ofast")
#pragma GCC optimise("unroll-loops")
using namespace std;
const int N = 200000 + 10;
const long long MOD = 1000000000 + 7;
const long long INF = 1000000000000000000;
const long long LOG = 25;
long long a00, a01, a10, a11, cnt0, cnt1;
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  cin >> a00 >> a01 >> a10 >> a11;
  if (a00 == 0 && a01 == 0 && a10 == 0 && a11 == 0) {
    cout << 0;
    return 0;
  }
  long int t0 = 0, t1 = 0, n0 = 0, n1 = 0;
  while (n0 + t0 <= a00) {
    n0 += t0;
    ++t0;
  }
  while (n1 + t1 <= a11) {
    n1 += t1;
    ++t1;
  }
  if (a10 == 0 && a01 == 0 && a00 == 0) t0 = 0;
  if (a11 == 0 && a10 == 0 && a01 == 0) t1 = 0;
  if (t0 * t1 != a10 + a01 || n0 != a00 || n1 != a11) {
    cout << "Impossible";
    return 0;
  }
  long long int len = t0 + t1;
  while (len--) {
    if (a01 >= t1) {
      cout << 0;
      a01 -= t1;
      t0--;
    } else {
      cout << 1;
      a10 -= t0;
      t1--;
    }
  }
  return 0;
}

### Prompt

Please provide a Cpp coded solution 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>
#pragma GCC optimise("ofast")
#pragma GCC optimise("unroll-loops")
using namespace std;
const int N = 200000 + 10;
const long long MOD = 1000000000 + 7;
const long long INF = 1000000000000000000;
const long long LOG = 25;
long long a00, a01, a10, a11, cnt0, cnt1;
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  cin >> a00 >> a01 >> a10 >> a11;
  if (a00 == 0 && a01 == 0 && a10 == 0 && a11 == 0) {
    cout << 0;
    return 0;
  }
  long int t0 = 0, t1 = 0, n0 = 0, n1 = 0;
  while (n0 + t0 <= a00) {
    n0 += t0;
    ++t0;
  }
  while (n1 + t1 <= a11) {
    n1 += t1;
    ++t1;
  }
  if (a10 == 0 && a01 == 0 && a00 == 0) t0 = 0;
  if (a11 == 0 && a10 == 0 && a01 == 0) t1 = 0;
  if (t0 * t1 != a10 + a01 || n0 != a00 || n1 != a11) {
    cout << "Impossible";
    return 0;
  }
  long long int len = t0 + t1;
  while (len--) {
    if (a01 >= t1) {
      cout << 0;
      a01 -= t1;
      t0--;
    } else {
      cout << 1;
      a10 -= t0;
      t1--;
    }
  }
  return 0;
}

```