#include <bits/stdc++.h>
using namespace std;
int arr[100000];
int main() {
  long long a, b, c, d;
  while (scanf("%lld%lld%lld%lld", &a, &b, &c, &d) != EOF) {
    memset(arr, 0, sizeof(arr));
    if (a + b + c + d == 0) {
      cout << 1 << endl;
      continue;
    }
    if (b + c == 0)
      if (a > 0 && d > 0) {
        cout << "Impossible\n";
        continue;
      }
    long long x = 0, y = 0;
    if (b + c > 0) {
      x++;
      y++;
    }
    while (x * (x - 1) / 2 < a) x++;
    while (y * (y - 1) / 2 < d) y++;
    if (x * (x - 1) / 2 != a || y * (y - 1) / 2 != d) {
      cout << "Impossible\n";
      continue;
    }
    if (x * y != b + c) {
      cout << "Impossible\n";
      continue;
    }
    for (int i = 0; i < y; i++) {
      int z = min(x, c);
      arr[z]++;
      c -= z;
    }
    for (int i = 0; i < x; i++) {
      for (int j = 0; j < arr[x - i]; j++) cout << 1;
      cout << 0;
    }
    for (int i = 0; i < arr[0]; i++) cout << 1;
    cout << endl;
  }
  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;
int arr[100000];
int main() {
  long long a, b, c, d;
  while (scanf("%lld%lld%lld%lld", &a, &b, &c, &d) != EOF) {
    memset(arr, 0, sizeof(arr));
    if (a + b + c + d == 0) {
      cout << 1 << endl;
      continue;
    }
    if (b + c == 0)
      if (a > 0 && d > 0) {
        cout << "Impossible\n";
        continue;
      }
    long long x = 0, y = 0;
    if (b + c > 0) {
      x++;
      y++;
    }
    while (x * (x - 1) / 2 < a) x++;
    while (y * (y - 1) / 2 < d) y++;
    if (x * (x - 1) / 2 != a || y * (y - 1) / 2 != d) {
      cout << "Impossible\n";
      continue;
    }
    if (x * y != b + c) {
      cout << "Impossible\n";
      continue;
    }
    for (int i = 0; i < y; i++) {
      int z = min(x, c);
      arr[z]++;
      c -= z;
    }
    for (int i = 0; i < x; i++) {
      for (int j = 0; j < arr[x - i]; j++) cout << 1;
      cout << 0;
    }
    for (int i = 0; i < arr[0]; i++) cout << 1;
    cout << endl;
  }
  return 0;
}

```