#include <bits/stdc++.h>
using namespace std;
int ZZ, ZO, OZ, OO;
int Array[1000001];
int Count;
int main(void) {
  register int i;
  cin >> ZZ >> ZO >> OZ >> OO;
  register int ZeroCount, OneCount;
  ZeroCount = sqrt(2 * ZZ) + 1;
  OneCount = sqrt(2 * OO) + 1;
  if (ZeroCount * (ZeroCount - 1) / 2 != ZZ) {
    goto Impossible;
  }
  if (OneCount * (OneCount - 1) / 2 != OO) {
    goto Impossible;
  }
  if (ZZ && !ZO && !OZ && !OO) {
    for (i = 1; i <= ZeroCount; i++) {
      cout << 0;
    }
    cout << endl;
    return 0;
  }
  if (!ZZ & !ZO && !OZ && OO) {
    for (i = 1; i <= OneCount; i++) {
      cout << 1;
    }
    cout << endl;
    return 0;
  }
  if (!ZZ && !ZO && !OZ && !OO) {
    cout << 0 << endl;
    return 0;
  }
  if (ZeroCount * OneCount != ZO + OZ) {
    goto Impossible;
  }
  while (OZ) {
    if (OZ >= ZeroCount) {
      OZ -= ZeroCount;
      Array[++Count] = 1;
    } else {
      Array[++Count - OZ + ZeroCount] = 1;
      OZ = 0;
    }
  }
  for (i = 1; i <= OneCount - Count; i++) {
    Array[ZeroCount + OneCount - i + 1] = 1;
  }
  for (i = 1; i <= ZeroCount + OneCount; i++) {
    cout << Array[i];
  }
  cout << endl;
  return 0;
Impossible:
  cout << "Impossible" << endl;
  return 0;
}

### Prompt

Create a solution in Cpp for 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 ZZ, ZO, OZ, OO;
int Array[1000001];
int Count;
int main(void) {
  register int i;
  cin >> ZZ >> ZO >> OZ >> OO;
  register int ZeroCount, OneCount;
  ZeroCount = sqrt(2 * ZZ) + 1;
  OneCount = sqrt(2 * OO) + 1;
  if (ZeroCount * (ZeroCount - 1) / 2 != ZZ) {
    goto Impossible;
  }
  if (OneCount * (OneCount - 1) / 2 != OO) {
    goto Impossible;
  }
  if (ZZ && !ZO && !OZ && !OO) {
    for (i = 1; i <= ZeroCount; i++) {
      cout << 0;
    }
    cout << endl;
    return 0;
  }
  if (!ZZ & !ZO && !OZ && OO) {
    for (i = 1; i <= OneCount; i++) {
      cout << 1;
    }
    cout << endl;
    return 0;
  }
  if (!ZZ && !ZO && !OZ && !OO) {
    cout << 0 << endl;
    return 0;
  }
  if (ZeroCount * OneCount != ZO + OZ) {
    goto Impossible;
  }
  while (OZ) {
    if (OZ >= ZeroCount) {
      OZ -= ZeroCount;
      Array[++Count] = 1;
    } else {
      Array[++Count - OZ + ZeroCount] = 1;
      OZ = 0;
    }
  }
  for (i = 1; i <= OneCount - Count; i++) {
    Array[ZeroCount + OneCount - i + 1] = 1;
  }
  for (i = 1; i <= ZeroCount + OneCount; i++) {
    cout << Array[i];
  }
  cout << endl;
  return 0;
Impossible:
  cout << "Impossible" << endl;
  return 0;
}

```