#include <bits/stdc++.h>
using namespace std;
int a00, a11, a10, a01;
int max(int a, int b) { return a > b ? a : b; }
int main() {
  cin >> a00 >> a01 >> a10 >> a11;
  int num0 = -1, num1 = -1;
  for (int i = 1; i * (i - 1) <= 2 * max(a00, a11); i++) {
    if (i * (i - 1) == 2 * a00) num0 = i;
    if (i * (i - 1) == 2 * a11) num1 = i;
  }
  if ((num0 == -1) || (num1 == -1)) {
    cout << "Impossible";
    return 0;
  }
  if ((a01 == 0) && (a10 == 0)) {
    if ((a11 > 0) && (a00 > 0)) {
      cout << "Impossible";
    } else {
      if (a00 > 0) {
        for (int i = 0; i < num0; i++) {
          cout << "0";
        }
      } else {
        for (int i = 0; i < num1; i++) {
          cout << "1";
        }
      }
    }
    return 0;
  }
  if (a01 != num0 * num1 - a10) {
    cout << "Impossible";
    return 0;
  }
  string Res = "";
  for (int i = 0; i < num0; i++) {
    Res += "0";
  }
  int S = a01;
  while (S > num0) {
    Res += "1";
    num1--;
    S -= num0;
  }
  while (num1 > 0) {
    Res.insert(S, "1");
    S = 0;
    num1--;
  }
  cout << Res;
  return 0;
}

### Prompt

In cpp, your task is to solve 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;
int a00, a11, a10, a01;
int max(int a, int b) { return a > b ? a : b; }
int main() {
  cin >> a00 >> a01 >> a10 >> a11;
  int num0 = -1, num1 = -1;
  for (int i = 1; i * (i - 1) <= 2 * max(a00, a11); i++) {
    if (i * (i - 1) == 2 * a00) num0 = i;
    if (i * (i - 1) == 2 * a11) num1 = i;
  }
  if ((num0 == -1) || (num1 == -1)) {
    cout << "Impossible";
    return 0;
  }
  if ((a01 == 0) && (a10 == 0)) {
    if ((a11 > 0) && (a00 > 0)) {
      cout << "Impossible";
    } else {
      if (a00 > 0) {
        for (int i = 0; i < num0; i++) {
          cout << "0";
        }
      } else {
        for (int i = 0; i < num1; i++) {
          cout << "1";
        }
      }
    }
    return 0;
  }
  if (a01 != num0 * num1 - a10) {
    cout << "Impossible";
    return 0;
  }
  string Res = "";
  for (int i = 0; i < num0; i++) {
    Res += "0";
  }
  int S = a01;
  while (S > num0) {
    Res += "1";
    num1--;
    S -= num0;
  }
  while (num1 > 0) {
    Res.insert(S, "1");
    S = 0;
    num1--;
  }
  cout << Res;
  return 0;
}

```