#include <bits/stdc++.h>
using namespace std;
const int N = 1e6 + 3;
int str[N];
map<int, int> sum;
int main() {
  int a, b, c, d;
  scanf("%d%d%d%d", &a, &b, &c, &d);
  for (int i = 1, k = 0; k <= 1e9; k += i, i++) sum[k] = i;
  if (a == 0 && b == 0 && c == 0 && d == 0) {
    printf("0\n");
    return 0;
  }
  if (a == 0 && b == 0 && c == 0 && sum[d]) {
    for (int i = 0; i < sum[d]; i++) printf("1");
    printf("\n");
    return 0;
  }
  if (d == 0 && b == 0 && c == 0 && sum[a]) {
    for (int i = 0; i < sum[a]; i++) printf("0");
    printf("\n");
    return 0;
  }
  if (sum[a] == 0 || sum[d] == 0) {
    printf("Impossible\n");
    return 0;
  }
  int num0 = sum[a], num1 = sum[d], num = num0 + num1;
  if (b + c != num0 * num1) {
    printf("Impossible\n");
    return 0;
  }
  int l = 1 + b / num1, r = l + num1;
  for (int i = l; i < r; i++) str[i] = 1;
  str[r] = 1, str[r - b % num1] = 0;
  for (int i = 1; i <= num; i++) printf("%d", str[i]);
  printf("\n");
  return 0;
}

### Prompt

Generate 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;
const int N = 1e6 + 3;
int str[N];
map<int, int> sum;
int main() {
  int a, b, c, d;
  scanf("%d%d%d%d", &a, &b, &c, &d);
  for (int i = 1, k = 0; k <= 1e9; k += i, i++) sum[k] = i;
  if (a == 0 && b == 0 && c == 0 && d == 0) {
    printf("0\n");
    return 0;
  }
  if (a == 0 && b == 0 && c == 0 && sum[d]) {
    for (int i = 0; i < sum[d]; i++) printf("1");
    printf("\n");
    return 0;
  }
  if (d == 0 && b == 0 && c == 0 && sum[a]) {
    for (int i = 0; i < sum[a]; i++) printf("0");
    printf("\n");
    return 0;
  }
  if (sum[a] == 0 || sum[d] == 0) {
    printf("Impossible\n");
    return 0;
  }
  int num0 = sum[a], num1 = sum[d], num = num0 + num1;
  if (b + c != num0 * num1) {
    printf("Impossible\n");
    return 0;
  }
  int l = 1 + b / num1, r = l + num1;
  for (int i = l; i < r; i++) str[i] = 1;
  str[r] = 1, str[r - b % num1] = 0;
  for (int i = 1; i <= num; i++) printf("%d", str[i]);
  printf("\n");
  return 0;
}

```