#include <bits/stdc++.h>
using namespace std;
int now, k, a11, a10, a01, a00, x0, x1, i;
inline int read() {
  int x = 0, f = 1;
  char ch = getchar();
  while (ch < '0' || ch > '9') {
    if (ch == '-') f = -1;
    ch = getchar();
  }
  while (ch <= '9' && ch >= '0') x = x * 10 + ch - '0', ch = getchar();
  return x * f;
}
inline void write(int x) {
  if (x < 0) putchar('-'), x = -x;
  if (x >= 10) write(x / 10);
  putchar(x % 10 + '0');
}
int main() {
  a00 = read();
  a01 = read();
  a10 = read();
  a11 = read();
  if (a00 == 0 && a01 == 0 && a10 == 0 && a11 == 0) {
    puts("0");
    return 0;
  }
  x0 = sqrt(a00 * 2) + 1;
  if (x0 * (x0 - 1) / 2 != a00) {
    puts("Impossible");
    return 0;
  }
  if (a00 == 0 && a01 == 0 && a10 == 0) x0 = 0;
  x1 = sqrt(a11 * 2) + 1;
  if (x1 * (x1 - 1) / 2 != a11) {
    puts("Impossible");
    return 0;
  }
  if (a11 == 0 && a10 == 0 && a01 == 0) x1 = 0;
  if (x0 == 0) {
    if (a01 || a10) {
      puts("Impossible");
      return 0;
    }
    for (i = 1; i <= x1; i++) putchar('1');
    return 0;
  }
  if (x1 == 0) {
    if (a01 || a10) {
      puts("Impossible");
      return 0;
    }
    for (i = 1; i <= x0; i++) putchar('0');
    return 0;
  }
  if (a01 + a10 != x0 * x1) {
    puts("Impossible");
    return 0;
  }
  if (a00 == 0 && a11 == 0) {
    if (a10 && a01) {
      puts("Impossible");
      return 0;
    }
    if (a10)
      puts("10");
    else
      puts("01");
    return 0;
  }
  if (a00 == 0) {
    for (i = 1; i <= a10; i++) putchar('1');
    putchar('0');
    for (i = 1; i <= a01; i++) putchar('1');
    return 0;
  }
  if (a11 == 0) {
    for (i = 1; i <= a01; i++) putchar('0');
    putchar('1');
    for (i = 1; i <= a10; i++) putchar('0');
    return 0;
  }
  k = x1;
  now = 0;
  for (i = 1; i <= x1 + x0; i++) {
    if (now + k <= a01) {
      putchar('0');
      now += k;
    } else {
      putchar('1');
      k--;
    }
  }
}

### 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 now, k, a11, a10, a01, a00, x0, x1, i;
inline int read() {
  int x = 0, f = 1;
  char ch = getchar();
  while (ch < '0' || ch > '9') {
    if (ch == '-') f = -1;
    ch = getchar();
  }
  while (ch <= '9' && ch >= '0') x = x * 10 + ch - '0', ch = getchar();
  return x * f;
}
inline void write(int x) {
  if (x < 0) putchar('-'), x = -x;
  if (x >= 10) write(x / 10);
  putchar(x % 10 + '0');
}
int main() {
  a00 = read();
  a01 = read();
  a10 = read();
  a11 = read();
  if (a00 == 0 && a01 == 0 && a10 == 0 && a11 == 0) {
    puts("0");
    return 0;
  }
  x0 = sqrt(a00 * 2) + 1;
  if (x0 * (x0 - 1) / 2 != a00) {
    puts("Impossible");
    return 0;
  }
  if (a00 == 0 && a01 == 0 && a10 == 0) x0 = 0;
  x1 = sqrt(a11 * 2) + 1;
  if (x1 * (x1 - 1) / 2 != a11) {
    puts("Impossible");
    return 0;
  }
  if (a11 == 0 && a10 == 0 && a01 == 0) x1 = 0;
  if (x0 == 0) {
    if (a01 || a10) {
      puts("Impossible");
      return 0;
    }
    for (i = 1; i <= x1; i++) putchar('1');
    return 0;
  }
  if (x1 == 0) {
    if (a01 || a10) {
      puts("Impossible");
      return 0;
    }
    for (i = 1; i <= x0; i++) putchar('0');
    return 0;
  }
  if (a01 + a10 != x0 * x1) {
    puts("Impossible");
    return 0;
  }
  if (a00 == 0 && a11 == 0) {
    if (a10 && a01) {
      puts("Impossible");
      return 0;
    }
    if (a10)
      puts("10");
    else
      puts("01");
    return 0;
  }
  if (a00 == 0) {
    for (i = 1; i <= a10; i++) putchar('1');
    putchar('0');
    for (i = 1; i <= a01; i++) putchar('1');
    return 0;
  }
  if (a11 == 0) {
    for (i = 1; i <= a01; i++) putchar('0');
    putchar('1');
    for (i = 1; i <= a10; i++) putchar('0');
    return 0;
  }
  k = x1;
  now = 0;
  for (i = 1; i <= x1 + x0; i++) {
    if (now + k <= a01) {
      putchar('0');
      now += k;
    } else {
      putchar('1');
      k--;
    }
  }
}

```