#include <bits/stdc++.h>
using namespace std;
const int maxn = 1e6 + 5;
char ans[maxn];
int main() {
  long long x, y, z, h;
  scanf("%lld%lld%lld%lld", &x, &y, &z, &h);
  long long n = -1, m = -1;
  for (long long i = 1; i <= 1e5; i++) {
    if (i * (i - 1) / 2 == x) {
      n = i;
    }
    if (i * (i - 1) / 2 == h) {
      m = i;
    }
  }
  if (x == 0 && y == 0 && z == 0 && h == 0) {
    return 0 * printf("1\n");
  }
  if (n == 1) {
    if (y == 0 && z == 0) n = 0;
  }
  if (m == 1) {
    if (y == 0 && z == 0) m = 0;
  }
  if (m == -1 || n == -1) return 0 * printf("Impossible\n");
  ;
  if (x + y + z + h != (n + m) * (n + m - 1) / 2) {
    return 0 * printf("Impossible\n");
    ;
  }
  int len = 0;
  while (n || m) {
    if (n == 0) {
      ans[++len] = '1';
      m--;
    } else {
      if (y >= m) {
        ans[++len] = '0';
        n--;
        y -= m;
      } else {
        ans[++len] = '1';
        m--;
        x -= n;
      }
    }
  }
  if (x != 0 && y != 0 && n != 0 && m != 0) return 0 * printf("Impossible\n");
  ;
  ans[++len] = '\0';
  printf("%s", ans + 1);
}

### Prompt

Please provide a Cpp coded solution 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;
const int maxn = 1e6 + 5;
char ans[maxn];
int main() {
  long long x, y, z, h;
  scanf("%lld%lld%lld%lld", &x, &y, &z, &h);
  long long n = -1, m = -1;
  for (long long i = 1; i <= 1e5; i++) {
    if (i * (i - 1) / 2 == x) {
      n = i;
    }
    if (i * (i - 1) / 2 == h) {
      m = i;
    }
  }
  if (x == 0 && y == 0 && z == 0 && h == 0) {
    return 0 * printf("1\n");
  }
  if (n == 1) {
    if (y == 0 && z == 0) n = 0;
  }
  if (m == 1) {
    if (y == 0 && z == 0) m = 0;
  }
  if (m == -1 || n == -1) return 0 * printf("Impossible\n");
  ;
  if (x + y + z + h != (n + m) * (n + m - 1) / 2) {
    return 0 * printf("Impossible\n");
    ;
  }
  int len = 0;
  while (n || m) {
    if (n == 0) {
      ans[++len] = '1';
      m--;
    } else {
      if (y >= m) {
        ans[++len] = '0';
        n--;
        y -= m;
      } else {
        ans[++len] = '1';
        m--;
        x -= n;
      }
    }
  }
  if (x != 0 && y != 0 && n != 0 && m != 0) return 0 * printf("Impossible\n");
  ;
  ans[++len] = '\0';
  printf("%s", ans + 1);
}

```