#include <bits/stdc++.h>
using namespace std;
long long a, b, c, d;
long long first, second;
int main() {
  cin >> a >> c >> d >> b;
  if (a + b + c + d == 0) {
    puts("0");
    return 0;
  }
  first = second = -1;
  int ok = 0;
  for (long long i = 0; i * (i - 1) / 2 <= a; ++i)
    if (i * (i - 1) / 2 == a) {
      first = i;
      ok++;
      break;
    }
  for (long long i = 0; i * (i - 1) <= b * 2; ++i)
    if (i * (i - 1) / 2 == b) {
      second = i;
      ok++;
      break;
    }
  if (ok != 2) {
    puts("Impossible");
    return 0;
  }
  if (a == 0 && c + d != 0) first = 1;
  if (b == 0 && c + d != 0) second = 1;
  if (c + d != first * second) {
    puts("Impossible");
    return 0;
  }
  for (int i = (0), _for = (first + second); i < _for; ++i) {
    if (c >= second) {
      cout << 0;
      c -= second;
    } else {
      cout << 1;
      second--;
    }
  }
  printf("\n");
  return 0;
}

### Prompt

Your task is to create 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;
long long first, second;
int main() {
  cin >> a >> c >> d >> b;
  if (a + b + c + d == 0) {
    puts("0");
    return 0;
  }
  first = second = -1;
  int ok = 0;
  for (long long i = 0; i * (i - 1) / 2 <= a; ++i)
    if (i * (i - 1) / 2 == a) {
      first = i;
      ok++;
      break;
    }
  for (long long i = 0; i * (i - 1) <= b * 2; ++i)
    if (i * (i - 1) / 2 == b) {
      second = i;
      ok++;
      break;
    }
  if (ok != 2) {
    puts("Impossible");
    return 0;
  }
  if (a == 0 && c + d != 0) first = 1;
  if (b == 0 && c + d != 0) second = 1;
  if (c + d != first * second) {
    puts("Impossible");
    return 0;
  }
  for (int i = (0), _for = (first + second); i < _for; ++i) {
    if (c >= second) {
      cout << 0;
      c -= second;
    } else {
      cout << 1;
      second--;
    }
  }
  printf("\n");
  return 0;
}

```