#include <bits/stdc++.h>
using namespace std;
long long gcd(long long a, long long b) { return b == 0 ? a : gcd(b, a % b); }
const int MAXLEN = 100000;
int a00, a01, a10, a11;
char ret[MAXLEN + 1];
int solve(long long a) {
  int ret = (1 + (int)sqrt(1 + 8 * a)) / 2;
  return (long long)ret * (ret - 1) == 2 * a ? ret : -1;
}
void run() {
  scanf("%d%d%d%d", &a00, &a01, &a10, &a11);
  if (a00 == 0 && a01 == 0 && a10 == 0 && a11 == 0) {
    printf("0\n");
    return;
  }
  int len = solve((long long)a00 + a01 + a10 + a11), n0 = solve(a00),
      n1 = solve(a11);
  if (a00 == 0 && a01 == 0 && a10 == 0) n0 = 0;
  if (a11 == 0 && a01 == 0 && a10 == 0) n1 = 0;
  if (len == -1 || n0 == -1 || n1 == -1 || n0 + n1 != len) {
    printf("Impossible\n");
    return;
  }
  for (int i = (0); i < (len); ++i) {
    if (a01 >= n1) {
      ret[i] = '0';
      a01 -= n1;
      --n0;
    } else {
      ret[i] = '1';
      a10 -= n0;
      --n1;
    }
  }
  assert(a10 == 0 && n0 == 0 && n1 == 0);
  ret[len] = '\0';
  printf("%s\n", ret);
}
int main() {
  run();
  return 0;
}

### Prompt

Please provide a Cpp coded solution 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 gcd(long long a, long long b) { return b == 0 ? a : gcd(b, a % b); }
const int MAXLEN = 100000;
int a00, a01, a10, a11;
char ret[MAXLEN + 1];
int solve(long long a) {
  int ret = (1 + (int)sqrt(1 + 8 * a)) / 2;
  return (long long)ret * (ret - 1) == 2 * a ? ret : -1;
}
void run() {
  scanf("%d%d%d%d", &a00, &a01, &a10, &a11);
  if (a00 == 0 && a01 == 0 && a10 == 0 && a11 == 0) {
    printf("0\n");
    return;
  }
  int len = solve((long long)a00 + a01 + a10 + a11), n0 = solve(a00),
      n1 = solve(a11);
  if (a00 == 0 && a01 == 0 && a10 == 0) n0 = 0;
  if (a11 == 0 && a01 == 0 && a10 == 0) n1 = 0;
  if (len == -1 || n0 == -1 || n1 == -1 || n0 + n1 != len) {
    printf("Impossible\n");
    return;
  }
  for (int i = (0); i < (len); ++i) {
    if (a01 >= n1) {
      ret[i] = '0';
      a01 -= n1;
      --n0;
    } else {
      ret[i] = '1';
      a10 -= n0;
      --n1;
    }
  }
  assert(a10 == 0 && n0 == 0 && n1 == 0);
  ret[len] = '\0';
  printf("%s\n", ret);
}
int main() {
  run();
  return 0;
}

```