#include <bits/stdc++.h>
using namespace std;
const int N = 100005;
const int M = 100005;
const int inf = 1000000007;
const int mod = 1000000007;
int main() {
  int a00, a01, a10, a11, l, r;
  scanf("%d%d%d%d", &a00, &a01, &a10, &a11);
  l = 1 + (int)sqrt(2.0 * a00);
  r = 1 + (int)sqrt(2.0 * a11);
  if (a01 + a10 == 0) {
    l = a00 ? l : 0;
    r = a11 ? r : 0;
    if (a00 + a11 == 0) l = 1;
  }
  if (l * (l - 1) != 2 * a00 || r * (r - 1) != 2 * a11 || a01 + a10 != l * r) {
    puts("Impossible");
    return 0;
  }
  while (a01) {
    if (r > a01)
      printf("1"), r--;
    else
      printf("0"), l--, a01 -= r;
  }
  while (r--) printf("1");
  while (l--) printf("0");
  puts("");
  return 0;
}

### Prompt

Generate a Cpp solution 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;
const int N = 100005;
const int M = 100005;
const int inf = 1000000007;
const int mod = 1000000007;
int main() {
  int a00, a01, a10, a11, l, r;
  scanf("%d%d%d%d", &a00, &a01, &a10, &a11);
  l = 1 + (int)sqrt(2.0 * a00);
  r = 1 + (int)sqrt(2.0 * a11);
  if (a01 + a10 == 0) {
    l = a00 ? l : 0;
    r = a11 ? r : 0;
    if (a00 + a11 == 0) l = 1;
  }
  if (l * (l - 1) != 2 * a00 || r * (r - 1) != 2 * a11 || a01 + a10 != l * r) {
    puts("Impossible");
    return 0;
  }
  while (a01) {
    if (r > a01)
      printf("1"), r--;
    else
      printf("0"), l--, a01 -= r;
  }
  while (r--) printf("1");
  while (l--) printf("0");
  puts("");
  return 0;
}

```