#include <bits/stdc++.h>
using namespace std;
char ans[223456];
int a[2][2];
int judge(int num_zero, int num_one) {
  if (num_zero * num_one != a[0][1] + a[1][0] or
      (num_zero == 0 and num_one == 0))
    return 0;
  int n = num_zero + num_one;
  for (int i = 0; i < num_zero; ++i) {
    ans[i] = '0';
  }
  for (int i = num_zero; i < n; ++i) {
    ans[i] = '1';
  }
  for (int i = num_zero, j = a[1][0]; i < n; ++i) {
    if (j > num_zero) {
      swap(ans[i], ans[i - num_zero]);
      j -= num_zero;
    } else {
      swap(ans[i], ans[i - j]);
      break;
    }
  }
  ans[n] = '\0';
  return 1;
}
int main() {
  while (cin >> a[0][0] >> a[0][1] >> a[1][0] >> a[1][1]) {
    int num_zero = -1, num_one = -1;
    for (int i = 0; i < 640000; ++i) {
      if (i * i == 2 * a[0][0] + i) {
        num_zero = i;
        for (int j = 0; j < 640000; ++j) {
          if (j * j == 2 * a[1][1] + j) {
            num_one = j;
            if (judge(num_zero, num_one)) {
              cout << ans << endl;
              return 0;
            }
          }
        }
      }
    }
    cout << "Impossible" << endl;
  }
  return 0;
}

### 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;
char ans[223456];
int a[2][2];
int judge(int num_zero, int num_one) {
  if (num_zero * num_one != a[0][1] + a[1][0] or
      (num_zero == 0 and num_one == 0))
    return 0;
  int n = num_zero + num_one;
  for (int i = 0; i < num_zero; ++i) {
    ans[i] = '0';
  }
  for (int i = num_zero; i < n; ++i) {
    ans[i] = '1';
  }
  for (int i = num_zero, j = a[1][0]; i < n; ++i) {
    if (j > num_zero) {
      swap(ans[i], ans[i - num_zero]);
      j -= num_zero;
    } else {
      swap(ans[i], ans[i - j]);
      break;
    }
  }
  ans[n] = '\0';
  return 1;
}
int main() {
  while (cin >> a[0][0] >> a[0][1] >> a[1][0] >> a[1][1]) {
    int num_zero = -1, num_one = -1;
    for (int i = 0; i < 640000; ++i) {
      if (i * i == 2 * a[0][0] + i) {
        num_zero = i;
        for (int j = 0; j < 640000; ++j) {
          if (j * j == 2 * a[1][1] + j) {
            num_one = j;
            if (judge(num_zero, num_one)) {
              cout << ans << endl;
              return 0;
            }
          }
        }
      }
    }
    cout << "Impossible" << endl;
  }
  return 0;
}

```