#include <bits/stdc++.h>
using namespace std;
int abs(int a) { return a > 0 ? a : -a; }
int max(int a, int b, int c) { return max(a, max(b, c)); }
int min(int a, int b, int c) { return min(a, min(b, c)); }
int main() {
  long long a00, a01, a10, a11;
  cin >> a00 >> a01 >> a10 >> a11;
  if (a00 == 0 && a01 == 0 && a10 == 0 && a11 == 0) {
    printf("0\n");
    return 0;
  }
  bool flag00 = false, flag11 = false;
  long long n0 = 0, n1 = 0;
  for (long long i = 0;; i++) {
    long long c = i * (i - 1) / 2;
    if (c > a00 && c > a11) {
      break;
    }
    if (c == a00) {
      flag00 = true;
      n0 = i;
    }
    if (c == a11) {
      flag11 = true;
      n1 = i;
    }
  }
  if (a01 + a10 == 0) {
    if (n0 == 1) {
      n0 = 0;
    }
    if (n1 == 1) {
      n1 = 0;
    }
  }
  if ((!flag00 || !flag11) || (n0 * n1 != a01 + a10)) {
    printf("Impossible\n");
    return 0;
  }
  long long i0 = n0 + 1;
  for (long long i = 1; i <= n0; i++) {
    if (i * n1 > a01) {
      i0 = i - 1;
      break;
    }
    printf("0");
  }
  for (long long i = 1; i <= n1; i++) {
    printf("1");
    if (i0 * n1 + (n1 - i) == a01) {
      printf("0");
    }
  }
  for (long long i = i0 + 2; i <= n0; i++) {
    printf("0");
  }
  printf("\n");
}

### 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>
using namespace std;
int abs(int a) { return a > 0 ? a : -a; }
int max(int a, int b, int c) { return max(a, max(b, c)); }
int min(int a, int b, int c) { return min(a, min(b, c)); }
int main() {
  long long a00, a01, a10, a11;
  cin >> a00 >> a01 >> a10 >> a11;
  if (a00 == 0 && a01 == 0 && a10 == 0 && a11 == 0) {
    printf("0\n");
    return 0;
  }
  bool flag00 = false, flag11 = false;
  long long n0 = 0, n1 = 0;
  for (long long i = 0;; i++) {
    long long c = i * (i - 1) / 2;
    if (c > a00 && c > a11) {
      break;
    }
    if (c == a00) {
      flag00 = true;
      n0 = i;
    }
    if (c == a11) {
      flag11 = true;
      n1 = i;
    }
  }
  if (a01 + a10 == 0) {
    if (n0 == 1) {
      n0 = 0;
    }
    if (n1 == 1) {
      n1 = 0;
    }
  }
  if ((!flag00 || !flag11) || (n0 * n1 != a01 + a10)) {
    printf("Impossible\n");
    return 0;
  }
  long long i0 = n0 + 1;
  for (long long i = 1; i <= n0; i++) {
    if (i * n1 > a01) {
      i0 = i - 1;
      break;
    }
    printf("0");
  }
  for (long long i = 1; i <= n1; i++) {
    printf("1");
    if (i0 * n1 + (n1 - i) == a01) {
      printf("0");
    }
  }
  for (long long i = i0 + 2; i <= n0; i++) {
    printf("0");
  }
  printf("\n");
}

```