#include <bits/stdc++.h>
int main() {
  {
    int a[4];
    scanf("%d%d%d%d", a, a + 1, a + 2, a + 3);
    if (a[0] + a[1] + a[2] + a[3] == 0) {
      putchar('0');
      return 0;
    }
    int s0 = sqrt(a[0] <<= 1) + 1;
    int s1 = sqrt(a[3] <<= 1) + 1;
    if (a[1] + a[2] == 0) {
      if (s0 == 1) s0 = 0;
      if (s1 == 1) s1 = 0;
    }
    if (a[0] != s0 * (s0 - 1) || a[3] != s1 * (s1 - 1) ||
        a[1] + a[2] != s0 * s1) {
      puts("Impossible");
    } else {
      while (s0 && s1) {
        while (a[2] >= s0) {
          putchar('1');
          a[2] -= s0;
          s1--;
        }
        while (a[2] < s0) {
          putchar('0');
          s0--;
        }
      }
      while (s0) {
        putchar('0');
        s0--;
      }
      while (s1) {
        putchar('1');
        s1--;
      }
    }
  }
  return 0;
}

### Prompt

Your task is to create 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>
int main() {
  {
    int a[4];
    scanf("%d%d%d%d", a, a + 1, a + 2, a + 3);
    if (a[0] + a[1] + a[2] + a[3] == 0) {
      putchar('0');
      return 0;
    }
    int s0 = sqrt(a[0] <<= 1) + 1;
    int s1 = sqrt(a[3] <<= 1) + 1;
    if (a[1] + a[2] == 0) {
      if (s0 == 1) s0 = 0;
      if (s1 == 1) s1 = 0;
    }
    if (a[0] != s0 * (s0 - 1) || a[3] != s1 * (s1 - 1) ||
        a[1] + a[2] != s0 * s1) {
      puts("Impossible");
    } else {
      while (s0 && s1) {
        while (a[2] >= s0) {
          putchar('1');
          a[2] -= s0;
          s1--;
        }
        while (a[2] < s0) {
          putchar('0');
          s0--;
        }
      }
      while (s0) {
        putchar('0');
        s0--;
      }
      while (s1) {
        putchar('1');
        s1--;
      }
    }
  }
  return 0;
}

```