#include <bits/stdc++.h>
using namespace std;
long long int F(long long int a) {
  long long int i = 1;
  for (; i * (i - 1) < 2 * a; i++)
    ;
  if (i * (i - 1) != 2 * a)
    return -1;
  else
    return i;
}
int main() {
  long long int a, b, c, d;
  while (scanf("%I64d%I64d%I64d%I64d", &a, &b, &c, &d) == 4) {
    long long int x = F(a), y = F(d);
    if (a == 0) {
      if (b == 0 && c == 0)
        x = 0;
      else
        x = 1;
    }
    if (d == 0) {
      if (b == 0 && c == 0)
        y = 0;
      else
        y = 1;
    }
    if (x == -1 || y == -1)
      puts("Impossible");
    else if (b + c != x * y)
      puts("Impossible");
    else if (x + y > 1000000)
      puts("Impossible");
    else if (!a && !b && !c && !d)
      puts("0");
    else {
      long long int i = 0, j = 0;
      for (; i < x; i++) {
        while (c >= x - i && j < y) printf("1"), c -= (x - i), j++;
        printf("0");
      }
      for (; j < y; j++) printf("1");
      puts("");
    }
  }
  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;
long long int F(long long int a) {
  long long int i = 1;
  for (; i * (i - 1) < 2 * a; i++)
    ;
  if (i * (i - 1) != 2 * a)
    return -1;
  else
    return i;
}
int main() {
  long long int a, b, c, d;
  while (scanf("%I64d%I64d%I64d%I64d", &a, &b, &c, &d) == 4) {
    long long int x = F(a), y = F(d);
    if (a == 0) {
      if (b == 0 && c == 0)
        x = 0;
      else
        x = 1;
    }
    if (d == 0) {
      if (b == 0 && c == 0)
        y = 0;
      else
        y = 1;
    }
    if (x == -1 || y == -1)
      puts("Impossible");
    else if (b + c != x * y)
      puts("Impossible");
    else if (x + y > 1000000)
      puts("Impossible");
    else if (!a && !b && !c && !d)
      puts("0");
    else {
      long long int i = 0, j = 0;
      for (; i < x; i++) {
        while (c >= x - i && j < y) printf("1"), c -= (x - i), j++;
        printf("0");
      }
      for (; j < y; j++) printf("1");
      puts("");
    }
  }
  return 0;
}

```