#include <bits/stdc++.h>
using namespace std;
long long solve(long long x) {
  x *= 2;
  long long l = 0, r = x, ans = 0;
  while (l <= r) {
    long long mid = (l + r) >> 1;
    if (mid * (mid - 1) <= x)
      l = mid + 1, ans = mid;
    else
      r = mid - 1;
  }
  if (ans * (ans - 1) != x) return -1;
  return ans;
}
char s[1000005];
int main() {
  long long a00, a01, a10, a11;
  cin >> a00 >> a01 >> a10 >> a11;
  if (a00 == 0 && a01 == 0 && a10 == 0 && a11 == 0) {
    puts("0");
    return 0;
  }
  long long cnt0 = solve(a00), cnt1 = solve(a11);
  if (a01 + a10 != 0) {
    if (cnt0 * cnt1 == 0) {
      if (cnt0 == 0)
        cnt0 = 1;
      else
        cnt1 = 1;
    }
    if (cnt0 * cnt1 == 0) {
      if (cnt0 == 0)
        cnt0 = 1;
      else
        cnt1 = 1;
    }
  }
  if (cnt0 == -1 || cnt1 == -1) {
    puts("Impossible");
    return 0;
  }
  if (a01 + a10 != cnt0 * cnt1) {
    puts("Impossible");
    return 0;
  }
  int cnt = cnt0, check01 = 0, i, ans1 = 0;
  for (i = 0; check01 < a01;) {
    while (a01 - check01 >= cnt) s[i++] = '1', check01 += cnt, ans1++;
    s[i++] = '0', cnt--;
  }
  while (cnt--) s[i++] = '0';
  while (ans1 < cnt1) s[i++] = '1', ans1++;
  while (i > 0) putchar(s[--i]);
}

### Prompt

Develop a solution in Cpp to the problem described below:

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 solve(long long x) {
  x *= 2;
  long long l = 0, r = x, ans = 0;
  while (l <= r) {
    long long mid = (l + r) >> 1;
    if (mid * (mid - 1) <= x)
      l = mid + 1, ans = mid;
    else
      r = mid - 1;
  }
  if (ans * (ans - 1) != x) return -1;
  return ans;
}
char s[1000005];
int main() {
  long long a00, a01, a10, a11;
  cin >> a00 >> a01 >> a10 >> a11;
  if (a00 == 0 && a01 == 0 && a10 == 0 && a11 == 0) {
    puts("0");
    return 0;
  }
  long long cnt0 = solve(a00), cnt1 = solve(a11);
  if (a01 + a10 != 0) {
    if (cnt0 * cnt1 == 0) {
      if (cnt0 == 0)
        cnt0 = 1;
      else
        cnt1 = 1;
    }
    if (cnt0 * cnt1 == 0) {
      if (cnt0 == 0)
        cnt0 = 1;
      else
        cnt1 = 1;
    }
  }
  if (cnt0 == -1 || cnt1 == -1) {
    puts("Impossible");
    return 0;
  }
  if (a01 + a10 != cnt0 * cnt1) {
    puts("Impossible");
    return 0;
  }
  int cnt = cnt0, check01 = 0, i, ans1 = 0;
  for (i = 0; check01 < a01;) {
    while (a01 - check01 >= cnt) s[i++] = '1', check01 += cnt, ans1++;
    s[i++] = '0', cnt--;
  }
  while (cnt--) s[i++] = '0';
  while (ans1 < cnt1) s[i++] = '1', ans1++;
  while (i > 0) putchar(s[--i]);
}

```