#include <bits/stdc++.h>
#pragma comment(linker, "/STACK:102400000,102400000")
using namespace std;
const int lowbit(int x) { return x & -x; }
const double eps = 1e-8;
const int INF = 1e9 + 7;
const long long inf = (1LL << 62);
const int MOD = 1e9 + 7;
const long long mod = (1LL << 32);
const int N = 110;
const int M = 100010;
const int maxn = 1001;
template <class T1, class T2>
inline void getmax(T1 &a, T2 b) {
  if (b > a) a = b;
}
template <class T1, class T2>
inline void getmin(T1 &a, T2 b) {
  if (b < a) a = b;
}
int read() {
  int v = 0, f = 1;
  char c = getchar();
  while (c < 48 || 57 < c) {
    if (c == '-') f = -1;
    c = getchar();
  }
  while (48 <= c && c <= 57) v = v * 10 + c - 48, c = getchar();
  return v * f;
}
long long a00, a01, a10, a11;
int main() {
  long long n, m;
  cin >> a00 >> a01 >> a10 >> a11;
  n = (1 + (int)(sqrt(1 + 8 * a00))) / 2;
  m = (1 + (int)(sqrt(1 + 8 * a11))) / 2;
  if (a00 == 0 && a01 == 0 && a10 == 0 && a11 == 0) {
    cout << 0;
    return 0;
  }
  if (a01 == 0 && a10 == 0) {
    if (a00 == 0)
      n = 0;
    else
      m = 0;
  }
  if (n * (n - 1) != 2 * a00 || m * (m - 1) != 2 * a11 || a01 + a10 != n * m) {
    cout << "Impossible";
    return 0;
  }
  while (n + m) {
    if (a01 >= m) {
      cout << 0;
      a01 -= m;
      --n;
    } else {
      cout << 1;
      a10 -= n;
      --m;
    }
  }
  return 0;
}

### Prompt

Your task is to create 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>
#pragma comment(linker, "/STACK:102400000,102400000")
using namespace std;
const int lowbit(int x) { return x & -x; }
const double eps = 1e-8;
const int INF = 1e9 + 7;
const long long inf = (1LL << 62);
const int MOD = 1e9 + 7;
const long long mod = (1LL << 32);
const int N = 110;
const int M = 100010;
const int maxn = 1001;
template <class T1, class T2>
inline void getmax(T1 &a, T2 b) {
  if (b > a) a = b;
}
template <class T1, class T2>
inline void getmin(T1 &a, T2 b) {
  if (b < a) a = b;
}
int read() {
  int v = 0, f = 1;
  char c = getchar();
  while (c < 48 || 57 < c) {
    if (c == '-') f = -1;
    c = getchar();
  }
  while (48 <= c && c <= 57) v = v * 10 + c - 48, c = getchar();
  return v * f;
}
long long a00, a01, a10, a11;
int main() {
  long long n, m;
  cin >> a00 >> a01 >> a10 >> a11;
  n = (1 + (int)(sqrt(1 + 8 * a00))) / 2;
  m = (1 + (int)(sqrt(1 + 8 * a11))) / 2;
  if (a00 == 0 && a01 == 0 && a10 == 0 && a11 == 0) {
    cout << 0;
    return 0;
  }
  if (a01 == 0 && a10 == 0) {
    if (a00 == 0)
      n = 0;
    else
      m = 0;
  }
  if (n * (n - 1) != 2 * a00 || m * (m - 1) != 2 * a11 || a01 + a10 != n * m) {
    cout << "Impossible";
    return 0;
  }
  while (n + m) {
    if (a01 >= m) {
      cout << 0;
      a01 -= m;
      --n;
    } else {
      cout << 1;
      a10 -= n;
      --m;
    }
  }
  return 0;
}

```