#include <bits/stdc++.h>
using namespace std;
char str[1000005];
int main() {
  long long a, b, c, d;
  scanf("%I64d%I64d%I64d%I64d", &a, &b, &c, &d);
  a *= 2;
  d *= 2;
  long long k1 = sqrt(a);
  long long k2 = sqrt(d);
  if (k1 * (k1 + 1) != a || k2 * (k2 + 1) != d) {
    puts("Impossible");
    return 0;
  }
  if (a == 0 && b == 0 && c == 0 && d == 0) {
    puts("0");
    return 0;
  }
  if (a == 0 && b == 0 && c == 0 && d) {
    for (int i = 1; i <= k2 + 1; i++) str[i] = '1';
    puts(str + 1);
    return 0;
  }
  if (a && b == 0 && c == 0 && d == 0) {
    for (int i = 1; i <= k1 + 1; i++) str[i] = '0';
    puts(str + 1);
    return 0;
  }
  if ((k1 + 1) * (k2 + 1) != b + c) {
    puts("Impossible");
    return 0;
  }
  k1++, k2++;
  long long cc = b / k2, e = b % k2;
  for (int i = 1; i <= k1 + k2; i++) str[i] = '0';
  for (int i = cc + 1; i <= cc + k2; i++) str[i] = '1';
  if (e) {
    str[cc + k2 + 1] = '1';
    str[cc + k2 + 1 - e] = '0';
  }
  puts(str + 1);
  return 0;
}

### Prompt

Please formulate 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;
char str[1000005];
int main() {
  long long a, b, c, d;
  scanf("%I64d%I64d%I64d%I64d", &a, &b, &c, &d);
  a *= 2;
  d *= 2;
  long long k1 = sqrt(a);
  long long k2 = sqrt(d);
  if (k1 * (k1 + 1) != a || k2 * (k2 + 1) != d) {
    puts("Impossible");
    return 0;
  }
  if (a == 0 && b == 0 && c == 0 && d == 0) {
    puts("0");
    return 0;
  }
  if (a == 0 && b == 0 && c == 0 && d) {
    for (int i = 1; i <= k2 + 1; i++) str[i] = '1';
    puts(str + 1);
    return 0;
  }
  if (a && b == 0 && c == 0 && d == 0) {
    for (int i = 1; i <= k1 + 1; i++) str[i] = '0';
    puts(str + 1);
    return 0;
  }
  if ((k1 + 1) * (k2 + 1) != b + c) {
    puts("Impossible");
    return 0;
  }
  k1++, k2++;
  long long cc = b / k2, e = b % k2;
  for (int i = 1; i <= k1 + k2; i++) str[i] = '0';
  for (int i = cc + 1; i <= cc + k2; i++) str[i] = '1';
  if (e) {
    str[cc + k2 + 1] = '1';
    str[cc + k2 + 1 - e] = '0';
  }
  puts(str + 1);
  return 0;
}

```