#include <bits/stdc++.h>
using namespace std;
const int maxn = 200000 + 10;
int a, b, c, d, ans[maxn];
int main() {
  cin >> a >> b >> c >> d;
  if (a == 0 && b == 0 && c == 0 && d == 0) {
    puts("0");
    return 0;
  }
  int x = -1, y = -1;
  for (int i = 1; i <= 100000; i++)
    if ((long long)i * (i - 1) / 2 == a) x = i;
  for (int i = 1; i <= 100000; i++)
    if ((long long)i * (i - 1) / 2 == d) y = i;
  if (x == 1 && b == 0 && c == 0) x = 0;
  if (y == 1 && b == 0 && c == 0) y = 0;
  if (x == -1 || y == -1) {
    puts("Impossible");
    return 0;
  }
  int zero = 0, one = 0, sum0 = 0, sum1 = 0;
  for (int i = 1; i <= x + y; i++) {
    if (sum0 + (y - one) <= b && zero <= x) {
      sum0 += y - one;
      zero++;
      ans[i] = 0;
    } else {
      if (sum1 + (x - zero) > c || one >= y) {
        puts("Impossible");
        return 0;
      }
      sum1 += x - zero;
      one++;
      ans[i] = 1;
    }
  }
  if (sum0 != b || sum1 != c) {
    puts("Impossible");
    return 0;
  }
  for (int i = 1; i <= x + y; i++) printf("%d", ans[i]);
  return 0;
}

### 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 = 200000 + 10;
int a, b, c, d, ans[maxn];
int main() {
  cin >> a >> b >> c >> d;
  if (a == 0 && b == 0 && c == 0 && d == 0) {
    puts("0");
    return 0;
  }
  int x = -1, y = -1;
  for (int i = 1; i <= 100000; i++)
    if ((long long)i * (i - 1) / 2 == a) x = i;
  for (int i = 1; i <= 100000; i++)
    if ((long long)i * (i - 1) / 2 == d) y = i;
  if (x == 1 && b == 0 && c == 0) x = 0;
  if (y == 1 && b == 0 && c == 0) y = 0;
  if (x == -1 || y == -1) {
    puts("Impossible");
    return 0;
  }
  int zero = 0, one = 0, sum0 = 0, sum1 = 0;
  for (int i = 1; i <= x + y; i++) {
    if (sum0 + (y - one) <= b && zero <= x) {
      sum0 += y - one;
      zero++;
      ans[i] = 0;
    } else {
      if (sum1 + (x - zero) > c || one >= y) {
        puts("Impossible");
        return 0;
      }
      sum1 += x - zero;
      one++;
      ans[i] = 1;
    }
  }
  if (sum0 != b || sum1 != c) {
    puts("Impossible");
    return 0;
  }
  for (int i = 1; i <= x + y; i++) printf("%d", ans[i]);
  return 0;
}

```