#include <bits/stdc++.h>
int calc(int x) {
  long long det = 8ll * x + 1;
  int t = (int)(sqrt(det) + 0.5);
  if (1ll * t * t != det) return -1;
  return (t + 1) / 2;
}
void print(char ch, int k) {
  for (int i = 1; i <= k; i++) putchar(ch);
}
int main() {
  int a, b, c, d;
  scanf("%d%d%d%d", &a, &b, &c, &d);
  int p = calc(a), q = calc(d);
  if (p == -1 || q == -1) {
    puts("Impossible");
    return 0;
  }
  if ((!a || !d) && b + c == 0) {
    if (!a && !d)
      putchar('0');
    else if (a)
      print('0', p);
    else
      print('1', q);
    putchar('\n');
  } else if (1ll * p * q != b + c)
    puts("Impossible");
  else {
    print('0', b / q);
    print('1', q - b % q);
    if (b / q < p) putchar('0');
    print('1', b % q);
    print('0', p - b / q - 1);
    putchar('\n');
  }
  return 0;
}

### Prompt

Create a solution in cpp for 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>
int calc(int x) {
  long long det = 8ll * x + 1;
  int t = (int)(sqrt(det) + 0.5);
  if (1ll * t * t != det) return -1;
  return (t + 1) / 2;
}
void print(char ch, int k) {
  for (int i = 1; i <= k; i++) putchar(ch);
}
int main() {
  int a, b, c, d;
  scanf("%d%d%d%d", &a, &b, &c, &d);
  int p = calc(a), q = calc(d);
  if (p == -1 || q == -1) {
    puts("Impossible");
    return 0;
  }
  if ((!a || !d) && b + c == 0) {
    if (!a && !d)
      putchar('0');
    else if (a)
      print('0', p);
    else
      print('1', q);
    putchar('\n');
  } else if (1ll * p * q != b + c)
    puts("Impossible");
  else {
    print('0', b / q);
    print('1', q - b % q);
    if (b / q < p) putchar('0');
    print('1', b % q);
    print('0', p - b / q - 1);
    putchar('\n');
  }
  return 0;
}

```