#include <bits/stdc++.h>
using namespace std;
int c[1000000];
int main() {
  long long a00, a01, a10, a11;
  cin >> a00 >> a01 >> a10 >> a11;
  long long na = sqrt(1 + 8 * a00);
  na = (na + 1) / 2;
  long long nb = sqrt(1 + 8 * a11);
  nb = (nb + 1) / 2;
  long long t = na * (na - 1);
  t /= 2;
  if (t != a00) {
    printf("Impossible\n");
    return 0;
  }
  t = nb * (nb - 1);
  t /= 2;
  if (t != a11) {
    printf("Impossible\n");
    return 0;
  }
  if (a01 == 0 && a10 == 0) {
    if (a00 > 0 && a11 > 0)
      printf("Impossible\n");
    else if (a00) {
      while (na--) printf("0");
      printf("\n");
    } else if (a11) {
      while (nb--) printf("1");
      printf("\n");
    } else
      printf("1\n");
    return 0;
  }
  long long p = na * nb;
  if (p != a01 + a10) {
    printf("Impossible\n");
    return 0;
  }
  int i = 0;
  while (a10) {
    t = min(a10, na);
    c[i++] = t;
    a10 -= t;
  }
  i = 0;
  string ret = "";
  for (int j = na; j > 0; --j) {
    if (c[i] == j) {
      ret += "1";
      ++i;
      ++j;
    } else {
      ret += "0";
    }
  }
  for (; i < nb; ++i) ret += "1";
  cout << ret << "\n";
}

### 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 c[1000000];
int main() {
  long long a00, a01, a10, a11;
  cin >> a00 >> a01 >> a10 >> a11;
  long long na = sqrt(1 + 8 * a00);
  na = (na + 1) / 2;
  long long nb = sqrt(1 + 8 * a11);
  nb = (nb + 1) / 2;
  long long t = na * (na - 1);
  t /= 2;
  if (t != a00) {
    printf("Impossible\n");
    return 0;
  }
  t = nb * (nb - 1);
  t /= 2;
  if (t != a11) {
    printf("Impossible\n");
    return 0;
  }
  if (a01 == 0 && a10 == 0) {
    if (a00 > 0 && a11 > 0)
      printf("Impossible\n");
    else if (a00) {
      while (na--) printf("0");
      printf("\n");
    } else if (a11) {
      while (nb--) printf("1");
      printf("\n");
    } else
      printf("1\n");
    return 0;
  }
  long long p = na * nb;
  if (p != a01 + a10) {
    printf("Impossible\n");
    return 0;
  }
  int i = 0;
  while (a10) {
    t = min(a10, na);
    c[i++] = t;
    a10 -= t;
  }
  i = 0;
  string ret = "";
  for (int j = na; j > 0; --j) {
    if (c[i] == j) {
      ret += "1";
      ++i;
      ++j;
    } else {
      ret += "0";
    }
  }
  for (; i < nb; ++i) ret += "1";
  cout << ret << "\n";
}

```