#include <bits/stdc++.h>
using namespace std;
int a[100000];
vector<int> ans;
int main() {
  long long a01, a00, a11, a10;
  cin >> a00 >> a01 >> a10 >> a11;
  long long x = -1, y = -1, i;
  for (i = 1; i <= 100000; i++) {
    if (i * (i - 1) == 2 * a11) x = i;
    if (i * (i - 1) == 2 * a00) y = i;
  }
  if (a01 == 0 && a10 == 0) {
    if (a00 == 0 && a11 == 0) {
      cout << "1";
      return 0;
    }
    if (a11 == 0) {
      if (y != -1) {
        for (i = 0; i < y; i++) cout << "0";
      } else {
        cout << "Impossible" << endl;
      }
      return 0;
    }
    if (a00 == 0) {
      if (x != -1) {
        for (i = 0; i < x; i++) cout << "1";
      } else {
        cout << "Impossible" << endl;
      }
      return 0;
    }
  }
  if (x == -1 || y == -1) {
    cout << "Impossible" << endl;
    return 0;
  }
  if (a10 + a01 != x * y) {
    cout << "Impossible" << endl;
    return 0;
  }
  int ind = 0;
  while (a01 > y) {
    a[ind] = y;
    a01 -= y;
    ind++;
  }
  a[ind] = a01;
  sort(a, a + x);
  int cou = 0;
  for (i = 0; i < x; i++) {
    while (cou < a[i]) {
      ans.push_back(0);
      cou++;
    }
    ans.push_back(1);
  }
  while (ans.size() < x + y) ans.push_back(0);
  for (i = 0; i < ans.size(); i++) cout << ans[i];
}

### Prompt

Develop a solution in CPP 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>
using namespace std;
int a[100000];
vector<int> ans;
int main() {
  long long a01, a00, a11, a10;
  cin >> a00 >> a01 >> a10 >> a11;
  long long x = -1, y = -1, i;
  for (i = 1; i <= 100000; i++) {
    if (i * (i - 1) == 2 * a11) x = i;
    if (i * (i - 1) == 2 * a00) y = i;
  }
  if (a01 == 0 && a10 == 0) {
    if (a00 == 0 && a11 == 0) {
      cout << "1";
      return 0;
    }
    if (a11 == 0) {
      if (y != -1) {
        for (i = 0; i < y; i++) cout << "0";
      } else {
        cout << "Impossible" << endl;
      }
      return 0;
    }
    if (a00 == 0) {
      if (x != -1) {
        for (i = 0; i < x; i++) cout << "1";
      } else {
        cout << "Impossible" << endl;
      }
      return 0;
    }
  }
  if (x == -1 || y == -1) {
    cout << "Impossible" << endl;
    return 0;
  }
  if (a10 + a01 != x * y) {
    cout << "Impossible" << endl;
    return 0;
  }
  int ind = 0;
  while (a01 > y) {
    a[ind] = y;
    a01 -= y;
    ind++;
  }
  a[ind] = a01;
  sort(a, a + x);
  int cou = 0;
  for (i = 0; i < x; i++) {
    while (cou < a[i]) {
      ans.push_back(0);
      cou++;
    }
    ans.push_back(1);
  }
  while (ans.size() < x + y) ans.push_back(0);
  for (i = 0; i < ans.size(); i++) cout << ans[i];
}

```