#include <bits/stdc++.h>
using namespace std;
const int maxn = 1e5 + 10;
const int maxm = 4e5 + 10;
const long long mod = 1e9 + 7;
const int inf = 0x3ffffff;
const double eps = 1e-5;
int a00, a01, a10, a11;
int a[maxn];
map<long long, int> m;
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  cin >> a00 >> a01 >> a10 >> a11;
  long long i = 1;
  while (i * (i + 1) <= 2e9) {
    m[(i * (i + 1)) / 2] = i;
    i++;
  }
  m[0] = INT_MAX;
  if (m[a00] == 0 || m[a11] == 0)
    return cout << "Impossible", 0;
  else {
    int x = m[a00];
    int y = m[a11];
    if (x == INT_MAX) x = 0;
    if (y == INT_MAX) y = 0;
    if (a01 + a10 != (x + 1) * (y + 1)) {
      if (x == 0 && a01 == 0 && a10 == 0) {
        for (int i = 0; i < y + 1; i++) cout << "1";
      } else if (y == 0 && a01 == 0 && a10 == 0) {
        for (int i = 0; i < x + 1; i++) cout << "0";
      } else
        return cout << "Impossible", 0;
    } else {
      int t = 0, b = 0;
      while (a01 >= (x + 1)) {
        a01 -= (x + 1);
        b++;
      }
      while (a10 >= (x + 1)) {
        a10 -= (x + 1);
        t++;
      }
      string s;
      while (t--) s.push_back('1');
      for (int j = 1; j <= (x + 1); j++) {
        s.push_back('0');
        if (a01 == j) s.push_back('1');
      }
      while (b--) s.push_back('1');
      cout << s;
    }
  }
  return ~~(0 - 0);
}

### Prompt

Please create a solution in CPP 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;
const int maxn = 1e5 + 10;
const int maxm = 4e5 + 10;
const long long mod = 1e9 + 7;
const int inf = 0x3ffffff;
const double eps = 1e-5;
int a00, a01, a10, a11;
int a[maxn];
map<long long, int> m;
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  cin >> a00 >> a01 >> a10 >> a11;
  long long i = 1;
  while (i * (i + 1) <= 2e9) {
    m[(i * (i + 1)) / 2] = i;
    i++;
  }
  m[0] = INT_MAX;
  if (m[a00] == 0 || m[a11] == 0)
    return cout << "Impossible", 0;
  else {
    int x = m[a00];
    int y = m[a11];
    if (x == INT_MAX) x = 0;
    if (y == INT_MAX) y = 0;
    if (a01 + a10 != (x + 1) * (y + 1)) {
      if (x == 0 && a01 == 0 && a10 == 0) {
        for (int i = 0; i < y + 1; i++) cout << "1";
      } else if (y == 0 && a01 == 0 && a10 == 0) {
        for (int i = 0; i < x + 1; i++) cout << "0";
      } else
        return cout << "Impossible", 0;
    } else {
      int t = 0, b = 0;
      while (a01 >= (x + 1)) {
        a01 -= (x + 1);
        b++;
      }
      while (a10 >= (x + 1)) {
        a10 -= (x + 1);
        t++;
      }
      string s;
      while (t--) s.push_back('1');
      for (int j = 1; j <= (x + 1); j++) {
        s.push_back('0');
        if (a01 == j) s.push_back('1');
      }
      while (b--) s.push_back('1');
      cout << s;
    }
  }
  return ~~(0 - 0);
}

```