#include <bits/stdc++.h>
using namespace std;
long long a, b, c, d, hsh[1000010] = {0};
int main() {
  ios::sync_with_stdio(0);
  cin >> a >> b >> c >> d;
  long long zrs, ons;
  long long temp = sqrt(1 + 8 * d);
  if (temp * temp != 1 + 8 * d) {
    cout << "Impossible";
    return 0;
  }
  ons = (1 + temp) / 2;
  temp = sqrt(1 + 8 * a);
  if (temp * temp != 1 + 8 * a) {
    cout << "Impossible";
    return 0;
  }
  zrs = (1 + temp) / 2;
  if (d == 0 && a == 0) {
    if (b + c == 0) {
      zrs = 0;
      ons = 1;
    } else if (b + c == 1) {
      zrs = 1;
      ons = 1;
    }
  } else if (d == 0) {
    if (b + c == zrs)
      ons = 1;
    else if (b + c == 0)
      ons = 0;
  } else if (a == 0) {
    if (b + c == ons)
      zrs = 1;
    else if (b + c == 0)
      zrs = 0;
  }
  if (b + c != zrs * ons) {
    cout << "Impossible";
    return 0;
  }
  long long i = 0;
  while (c) {
    if (c > ons) {
      hsh[ons]++;
      c -= ons;
      i++;
    } else {
      hsh[c]++;
      c = 0;
      i++;
    }
  }
  hsh[0] += zrs - i;
  while (hsh[0]) {
    cout << 0;
    hsh[0]--;
  }
  for (long long i = 1; i <= ons; i++) {
    cout << 1;
    while (hsh[i]) {
      cout << 0;
      hsh[i]--;
    }
  }
  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;
long long a, b, c, d, hsh[1000010] = {0};
int main() {
  ios::sync_with_stdio(0);
  cin >> a >> b >> c >> d;
  long long zrs, ons;
  long long temp = sqrt(1 + 8 * d);
  if (temp * temp != 1 + 8 * d) {
    cout << "Impossible";
    return 0;
  }
  ons = (1 + temp) / 2;
  temp = sqrt(1 + 8 * a);
  if (temp * temp != 1 + 8 * a) {
    cout << "Impossible";
    return 0;
  }
  zrs = (1 + temp) / 2;
  if (d == 0 && a == 0) {
    if (b + c == 0) {
      zrs = 0;
      ons = 1;
    } else if (b + c == 1) {
      zrs = 1;
      ons = 1;
    }
  } else if (d == 0) {
    if (b + c == zrs)
      ons = 1;
    else if (b + c == 0)
      ons = 0;
  } else if (a == 0) {
    if (b + c == ons)
      zrs = 1;
    else if (b + c == 0)
      zrs = 0;
  }
  if (b + c != zrs * ons) {
    cout << "Impossible";
    return 0;
  }
  long long i = 0;
  while (c) {
    if (c > ons) {
      hsh[ons]++;
      c -= ons;
      i++;
    } else {
      hsh[c]++;
      c = 0;
      i++;
    }
  }
  hsh[0] += zrs - i;
  while (hsh[0]) {
    cout << 0;
    hsh[0]--;
  }
  for (long long i = 1; i <= ons; i++) {
    cout << 1;
    while (hsh[i]) {
      cout << 0;
      hsh[i]--;
    }
  }
  return 0;
}

```