#include <bits/stdc++.h>
using namespace std;
long long f(long long x) { return x * (x - 1) / 2; }
long long a, b, c, d, A, B;
int flag = 0;
int main() {
  cin >> a >> b >> c >> d;
  for (long long i = 0; f(i) <= a; i++) {
    if (f(i) == a) {
      for (long long j = 0; f(j) <= d; j++) {
        if (f(j) == d) {
          if (i * j == b + c) {
            A = i;
            B = j;
            flag = 1;
          }
        }
      }
    }
  }
  if (flag == 0) return puts("Impossible"), 0;
  if (A == 0 && B == 0) return puts("Impossible"), 0;
  int sum = A + B;
  for (int i = 0; i < sum; i++) {
    if (c >= A) {
      B--;
      c -= A;
      printf("1");
    } else {
      A--;
      printf("0");
    }
  }
  printf("\n");
  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) { return x * (x - 1) / 2; }
long long a, b, c, d, A, B;
int flag = 0;
int main() {
  cin >> a >> b >> c >> d;
  for (long long i = 0; f(i) <= a; i++) {
    if (f(i) == a) {
      for (long long j = 0; f(j) <= d; j++) {
        if (f(j) == d) {
          if (i * j == b + c) {
            A = i;
            B = j;
            flag = 1;
          }
        }
      }
    }
  }
  if (flag == 0) return puts("Impossible"), 0;
  if (A == 0 && B == 0) return puts("Impossible"), 0;
  int sum = A + B;
  for (int i = 0; i < sum; i++) {
    if (c >= A) {
      B--;
      c -= A;
      printf("1");
    } else {
      A--;
      printf("0");
    }
  }
  printf("\n");
  return 0;
}

```