#include <bits/stdc++.h>
using namespace std;
long long s[2000020];
long long Sqrt(long long k) {
  long long l = 1, r = k > 10000ll ? k / 100 : k;
  while (l <= r) {
    long long mid = (l + r) >> 1;
    if (mid * mid > k)
      r = mid - 1ll;
    else if (mid * mid < k)
      l = mid + 1ll;
    else if (mid * mid == k)
      return mid;
  }
  return -10ll;
}
long long solve(long long k) {
  k *= 2ll;
  return (Sqrt(1ll + 4 * k) - 1ll) / 2ll;
}
bool legal(long long x, long long y, long long b, long long c) {
  if (x < 0 || y < 0) return false;
  if (b + c == x * y) return true;
  if (b + c == 0 && (x == 1 || y == 1)) return true;
  return false;
}
int main() {
  long long a, b, c, d;
  cin >> a >> b >> c >> d;
  if (a < 0 || b < 0 || c < 0 || d < 0) {
    cout << "Impossible" << endl;
    return 0;
  }
  long long x = solve(a) + 1, y = solve(d) + 1;
  if (!legal(x, y, b, c)) {
    cout << "Impossible" << endl;
    return 0;
  }
  if (b + c == 0 && x == 1) x = 0;
  if (b + c == 0 && y == 1 && x != 0) y = 0;
  if (x == 0) {
    for (long long i = 1; i <= y; i++) cout << 1;
    return 0;
  }
  if (y == 0) {
    for (long long i = 1; i <= x; i++) cout << 0;
    return 0;
  }
  long long q = c / x;
  c %= x;
  for (long long i = 1; i <= q; i++) s[i] = 1;
  for (long long i = q + 1; i <= q + x; i++) s[i] = 0;
  for (long long i = q + x + 1; i <= x + y; i++) s[i] = 1;
  s[q + x + 1] = 0;
  s[q + x + 1 - c] = 1;
  for (long long i = 1; i <= x + y; i++) printf("%d", s[i]);
  return 0;
}

### Prompt

Your challenge is to write 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 s[2000020];
long long Sqrt(long long k) {
  long long l = 1, r = k > 10000ll ? k / 100 : k;
  while (l <= r) {
    long long mid = (l + r) >> 1;
    if (mid * mid > k)
      r = mid - 1ll;
    else if (mid * mid < k)
      l = mid + 1ll;
    else if (mid * mid == k)
      return mid;
  }
  return -10ll;
}
long long solve(long long k) {
  k *= 2ll;
  return (Sqrt(1ll + 4 * k) - 1ll) / 2ll;
}
bool legal(long long x, long long y, long long b, long long c) {
  if (x < 0 || y < 0) return false;
  if (b + c == x * y) return true;
  if (b + c == 0 && (x == 1 || y == 1)) return true;
  return false;
}
int main() {
  long long a, b, c, d;
  cin >> a >> b >> c >> d;
  if (a < 0 || b < 0 || c < 0 || d < 0) {
    cout << "Impossible" << endl;
    return 0;
  }
  long long x = solve(a) + 1, y = solve(d) + 1;
  if (!legal(x, y, b, c)) {
    cout << "Impossible" << endl;
    return 0;
  }
  if (b + c == 0 && x == 1) x = 0;
  if (b + c == 0 && y == 1 && x != 0) y = 0;
  if (x == 0) {
    for (long long i = 1; i <= y; i++) cout << 1;
    return 0;
  }
  if (y == 0) {
    for (long long i = 1; i <= x; i++) cout << 0;
    return 0;
  }
  long long q = c / x;
  c %= x;
  for (long long i = 1; i <= q; i++) s[i] = 1;
  for (long long i = q + 1; i <= q + x; i++) s[i] = 0;
  for (long long i = q + x + 1; i <= x + y; i++) s[i] = 1;
  s[q + x + 1] = 0;
  s[q + x + 1 - c] = 1;
  for (long long i = 1; i <= x + y; i++) printf("%d", s[i]);
  return 0;
}

```