#include <bits/stdc++.h>
using namespace std;
long long a, b, c, d, tot1, tot0;
int main() {
  cin >> a >> b >> c >> d;
  if (!a && !b && !c && !d) {
    puts("0");
    return 0;
  }
  if (!a && !b && !c)
    tot0 = 0;
  else
    tot0 = 1;
  if (!d && !b && !c)
    tot1 = 0;
  else
    tot1 = 1;
  if (a) tot0 = (int)(sqrt(a * 2)) + 1;
  if (d) tot1 = (int)(sqrt(d * 2)) + 1;
  if (tot0 * (tot0 - 1) / 2 != a || tot1 * (tot1 - 1) / 2 != d ||
      tot0 * tot1 != b + c) {
    puts("Impossible");
    return 0;
  }
  while (b) {
    if (b >= tot1) {
      cout << 0;
      b -= tot1;
      tot0--;
    } else if (c >= tot0) {
      cout << 1;
      c -= tot0;
      tot1--;
    }
  }
  while (tot1) cout << 1, tot1--;
  while (tot0) cout << 0, tot0--;
}

### Prompt

Your challenge is to write 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 a, b, c, d, tot1, tot0;
int main() {
  cin >> a >> b >> c >> d;
  if (!a && !b && !c && !d) {
    puts("0");
    return 0;
  }
  if (!a && !b && !c)
    tot0 = 0;
  else
    tot0 = 1;
  if (!d && !b && !c)
    tot1 = 0;
  else
    tot1 = 1;
  if (a) tot0 = (int)(sqrt(a * 2)) + 1;
  if (d) tot1 = (int)(sqrt(d * 2)) + 1;
  if (tot0 * (tot0 - 1) / 2 != a || tot1 * (tot1 - 1) / 2 != d ||
      tot0 * tot1 != b + c) {
    puts("Impossible");
    return 0;
  }
  while (b) {
    if (b >= tot1) {
      cout << 0;
      b -= tot1;
      tot0--;
    } else if (c >= tot0) {
      cout << 1;
      c -= tot0;
      tot1--;
    }
  }
  while (tot1) cout << 1, tot1--;
  while (tot0) cout << 0, tot0--;
}

```