#include <bits/stdc++.h>
using namespace std;
int aa, ab, ba, bb;
int main() {
  cin >> aa >> ab >> ba >> bb;
  int a = -1;
  for (int i = 1; i <= 1000000; i++)
    if (1LL * i * (i - 1) / 2 == aa) {
      a = i;
      break;
    }
  if (a == -1) return printf("Impossible\n"), 0;
  if (ab == 0 && ba == 0 && bb == 0)
    return printf("%s\n", string(a, '0').c_str()), 0;
  int b = -1;
  for (int i = 1; i <= 1000000; i++)
    if (1LL * i * (i - 1) / 2 == bb) {
      b = i;
      break;
    }
  if (b == -1) return printf("Impossible\n"), 0;
  if (aa == 0 && ab == 0 && ba == 0)
    return printf("%s\n", string(b, '1').c_str()), 0;
  if (a == -1 || b == -1 || ab + ba != 1LL * a * b)
    return printf("Impossible\n"), 0;
  if (a == 0) {
    string s(b, '1');
    puts(s.c_str());
    return 0;
  }
  int p = ab / a;
  int q = ba / a;
  int r = ab % a;
  if (ab % a == 0 && ba % a == 0) {
    string s = string(q, '1') + string(a, '0') + string(p, '1');
    puts(s.c_str());
    return 0;
  }
  string s = string(q, '1') + string(r, '0') + "1" + string(a - r, '0') +
             string(p, '1');
  puts(s.c_str());
  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 aa, ab, ba, bb;
int main() {
  cin >> aa >> ab >> ba >> bb;
  int a = -1;
  for (int i = 1; i <= 1000000; i++)
    if (1LL * i * (i - 1) / 2 == aa) {
      a = i;
      break;
    }
  if (a == -1) return printf("Impossible\n"), 0;
  if (ab == 0 && ba == 0 && bb == 0)
    return printf("%s\n", string(a, '0').c_str()), 0;
  int b = -1;
  for (int i = 1; i <= 1000000; i++)
    if (1LL * i * (i - 1) / 2 == bb) {
      b = i;
      break;
    }
  if (b == -1) return printf("Impossible\n"), 0;
  if (aa == 0 && ab == 0 && ba == 0)
    return printf("%s\n", string(b, '1').c_str()), 0;
  if (a == -1 || b == -1 || ab + ba != 1LL * a * b)
    return printf("Impossible\n"), 0;
  if (a == 0) {
    string s(b, '1');
    puts(s.c_str());
    return 0;
  }
  int p = ab / a;
  int q = ba / a;
  int r = ab % a;
  if (ab % a == 0 && ba % a == 0) {
    string s = string(q, '1') + string(a, '0') + string(p, '1');
    puts(s.c_str());
    return 0;
  }
  string s = string(q, '1') + string(r, '0') + "1" + string(a - r, '0') +
             string(p, '1');
  puts(s.c_str());
  return 0;
}

```