#include <bits/stdc++.h>
using namespace std;
long long Find(long long x) {
  for (long long i = 1;; i++)
    if (i * (i - 1) == x)
      return i;
    else if (i * (i - 1) > x)
      return -1;
}
int main() {
  long long a, b, c, d;
  scanf("%lld%lld%lld%lld", &a, &b, &c, &d);
  long long sum = a + b + c + d;
  if (sum == 0) return puts("0"), 0;
  long long x = Find(a * 2);
  long long y = Find(d * 2);
  long long n = x + y;
  if (x == -1 || y == -1) return puts("Impossible"), 0;
  if (a + b + c == 0) {
    while (y--) putchar('1');
    return 0;
  }
  if (b + c + d == 0) {
    while (x--) putchar('0');
    return 0;
  }
  if (n * (n - 1) != sum * 2) return puts("Impossible"), 0;
  long long num = (n * (n - 1) / 2 - a - d - b) / x;
  while (num--) putchar('1'), --y;
  num = (n * (n - 1) / 2 - a - d - b) % x;
  for (long long i = 1, sz = x - num; i <= sz; i++) putchar('0'), --x;
  if (y) putchar('1'), --y;
  while (x--) putchar('0');
  while (y--) putchar('1');
}

### 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;
long long Find(long long x) {
  for (long long i = 1;; i++)
    if (i * (i - 1) == x)
      return i;
    else if (i * (i - 1) > x)
      return -1;
}
int main() {
  long long a, b, c, d;
  scanf("%lld%lld%lld%lld", &a, &b, &c, &d);
  long long sum = a + b + c + d;
  if (sum == 0) return puts("0"), 0;
  long long x = Find(a * 2);
  long long y = Find(d * 2);
  long long n = x + y;
  if (x == -1 || y == -1) return puts("Impossible"), 0;
  if (a + b + c == 0) {
    while (y--) putchar('1');
    return 0;
  }
  if (b + c + d == 0) {
    while (x--) putchar('0');
    return 0;
  }
  if (n * (n - 1) != sum * 2) return puts("Impossible"), 0;
  long long num = (n * (n - 1) / 2 - a - d - b) / x;
  while (num--) putchar('1'), --y;
  num = (n * (n - 1) / 2 - a - d - b) % x;
  for (long long i = 1, sz = x - num; i <= sz; i++) putchar('0'), --x;
  if (y) putchar('1'), --y;
  while (x--) putchar('0');
  while (y--) putchar('1');
}

```