#include <bits/stdc++.h>
using namespace std;
long long f(long long x) {
  if (x == 0) {
    return 0;
  }
  long long l = 1, h = x;
  while (l <= h) {
    long long m = (l + h) / 2;
    if (m * (m - 1) == x) {
      return m;
    } else if (m * (m - 1) < x) {
      l = m + 1;
    } else {
      h = m - 1;
    }
  }
  return -1;
}
int main() {
  while (true) {
    long long xs[4];
    for (int i = 0; i < 4; ++i) {
      cin >> xs[i];
    }
    if (!cin) {
      break;
    }
    long long m = f(2 * xs[0]), n = f(2 * xs[3]);
    if (xs[1] + xs[2] != 0) {
      m = (m == 0 ? 1 : m);
      n = (n == 0 ? 1 : n);
    }
    if (m == -1 || n == -1 || xs[1] + xs[2] != m * n) {
      cout << "Impossible" << endl;
      continue;
    }
    if (m == 0 && n == 0) {
      cout << "0" << endl;
      continue;
    }
    string res;
    int t = n, x = xs[2], y = n;
    while (x > 0) {
      if (x < t) {
        res += '1';
        --y;
        --t;
        continue;
      }
      int c = x / t;
      for (int i = 0; i < c; ++i) {
        x -= t;
        res += '0';
      }
    }
    for (int i = 0; i < y; ++i) {
      res += '1';
    }
    while (res.length() < m + n) {
      res += '0';
    }
    reverse(begin(res), end(res));
    cout << res << endl;
  }
  return 0;
}

### Prompt

Please create a solution in CPP 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 f(long long x) {
  if (x == 0) {
    return 0;
  }
  long long l = 1, h = x;
  while (l <= h) {
    long long m = (l + h) / 2;
    if (m * (m - 1) == x) {
      return m;
    } else if (m * (m - 1) < x) {
      l = m + 1;
    } else {
      h = m - 1;
    }
  }
  return -1;
}
int main() {
  while (true) {
    long long xs[4];
    for (int i = 0; i < 4; ++i) {
      cin >> xs[i];
    }
    if (!cin) {
      break;
    }
    long long m = f(2 * xs[0]), n = f(2 * xs[3]);
    if (xs[1] + xs[2] != 0) {
      m = (m == 0 ? 1 : m);
      n = (n == 0 ? 1 : n);
    }
    if (m == -1 || n == -1 || xs[1] + xs[2] != m * n) {
      cout << "Impossible" << endl;
      continue;
    }
    if (m == 0 && n == 0) {
      cout << "0" << endl;
      continue;
    }
    string res;
    int t = n, x = xs[2], y = n;
    while (x > 0) {
      if (x < t) {
        res += '1';
        --y;
        --t;
        continue;
      }
      int c = x / t;
      for (int i = 0; i < c; ++i) {
        x -= t;
        res += '0';
      }
    }
    for (int i = 0; i < y; ++i) {
      res += '1';
    }
    while (res.length() < m + n) {
      res += '0';
    }
    reverse(begin(res), end(res));
    cout << res << endl;
  }
  return 0;
}

```