#include <bits/stdc++.h>
using namespace std;
const int MAXN = 1e5 + 10, MOD = 1e9 + 7, INF = 1e9 + 5;
void imp() {
  cout << "Impossible\n";
  exit(0);
}
long long get_n(long long x) {
  for (long long i = 1; i < MAXN; i++)
    if (i * (i - 1) / 2 == x) return i;
  imp();
  return 0;
}
int main() {
  ios::sync_with_stdio(0), cin.tie(0), cout.tie(0);
  long long n1, n0, a00, a10, a01, a11;
  cin >> a00 >> a01 >> a10 >> a11;
  n0 = get_n(a00);
  n1 = get_n(a11);
  if (a01 + a10 == 0) {
    if (n0 > 1 && n1 > 1) imp();
    if (a11) {
      for (int i = 0; i < n1; i++) cout << '1';
      return 0;
    }
    if (a00) {
      for (int i = 0; i < n0; i++) cout << '0';
      return 0;
    }
    cout << '1';
    return 0;
  }
  if (n0 * n1 != a01 + a10) {
    imp();
  }
  long long n = n0 + n1;
  for (int i = 0; i < n; i++) {
    if (n0 && n1 <= a01) {
      cout << '0';
      n0--;
      a01 -= n1;
    } else {
      cout << '1';
      n1--;
      a10 -= n0;
    }
  }
  cout << '\n';
}

### 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;
const int MAXN = 1e5 + 10, MOD = 1e9 + 7, INF = 1e9 + 5;
void imp() {
  cout << "Impossible\n";
  exit(0);
}
long long get_n(long long x) {
  for (long long i = 1; i < MAXN; i++)
    if (i * (i - 1) / 2 == x) return i;
  imp();
  return 0;
}
int main() {
  ios::sync_with_stdio(0), cin.tie(0), cout.tie(0);
  long long n1, n0, a00, a10, a01, a11;
  cin >> a00 >> a01 >> a10 >> a11;
  n0 = get_n(a00);
  n1 = get_n(a11);
  if (a01 + a10 == 0) {
    if (n0 > 1 && n1 > 1) imp();
    if (a11) {
      for (int i = 0; i < n1; i++) cout << '1';
      return 0;
    }
    if (a00) {
      for (int i = 0; i < n0; i++) cout << '0';
      return 0;
    }
    cout << '1';
    return 0;
  }
  if (n0 * n1 != a01 + a10) {
    imp();
  }
  long long n = n0 + n1;
  for (int i = 0; i < n; i++) {
    if (n0 && n1 <= a01) {
      cout << '0';
      n0--;
      a01 -= n1;
    } else {
      cout << '1';
      n1--;
      a10 -= n0;
    }
  }
  cout << '\n';
}

```