#include <bits/stdc++.h>
using namespace std;
int a00, a01, a10, a11;
int a0, a1;
int main() {
  scanf("%d%d%d%d", &a00, &a01, &a10, &a11);
  if (a00 + a01 + a10 + a11 == 0) {
    printf("0\n");
    return 0;
  }
  if (a00 == 0) {
    if (a01 + a10 > 0)
      a0 = 1;
    else
      a0 = 0;
  } else {
    for (a0 = 1; a0 * (a0 - 1) / 2 < a00; ++a0)
      ;
    if (a0 * (a0 - 1) / 2 != a00) {
      printf("Impossible\n");
      return 0;
    }
  }
  if (a11 == 0) {
    if (a01 + a10 > 0)
      a1 = 1;
    else
      a1 = 0;
  } else {
    for (a1 = 1; a1 * (a1 - 1) / 2 < a11; ++a1)
      ;
    if (a1 * (a1 - 1) / 2 != a11) {
      printf("Impossible\n");
      return 0;
    }
  }
  if (a01 + a10 != a0 * a1) {
    printf("Impossible\n");
    return 0;
  }
  if (a1 == 0) {
    for (int i = 1; i <= a0; ++i) printf("0");
    printf("\n");
    return 0;
  }
  for (int i = 1; i <= a01 / a1; ++i) {
    printf("0");
    a0--;
  }
  for (int i = 1; i <= a1 - a01 % a1; ++i) printf("1");
  if (a0 > 0) {
    printf("0");
    a0--;
  }
  for (int i = 1; i <= a01 % a1; ++i) printf("1");
  for (int i = 1; i <= a0; ++i) printf("0");
  printf("\n");
}

### Prompt

Develop a solution in CPP 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;
int a00, a01, a10, a11;
int a0, a1;
int main() {
  scanf("%d%d%d%d", &a00, &a01, &a10, &a11);
  if (a00 + a01 + a10 + a11 == 0) {
    printf("0\n");
    return 0;
  }
  if (a00 == 0) {
    if (a01 + a10 > 0)
      a0 = 1;
    else
      a0 = 0;
  } else {
    for (a0 = 1; a0 * (a0 - 1) / 2 < a00; ++a0)
      ;
    if (a0 * (a0 - 1) / 2 != a00) {
      printf("Impossible\n");
      return 0;
    }
  }
  if (a11 == 0) {
    if (a01 + a10 > 0)
      a1 = 1;
    else
      a1 = 0;
  } else {
    for (a1 = 1; a1 * (a1 - 1) / 2 < a11; ++a1)
      ;
    if (a1 * (a1 - 1) / 2 != a11) {
      printf("Impossible\n");
      return 0;
    }
  }
  if (a01 + a10 != a0 * a1) {
    printf("Impossible\n");
    return 0;
  }
  if (a1 == 0) {
    for (int i = 1; i <= a0; ++i) printf("0");
    printf("\n");
    return 0;
  }
  for (int i = 1; i <= a01 / a1; ++i) {
    printf("0");
    a0--;
  }
  for (int i = 1; i <= a1 - a01 % a1; ++i) printf("1");
  if (a0 > 0) {
    printf("0");
    a0--;
  }
  for (int i = 1; i <= a01 % a1; ++i) printf("1");
  for (int i = 1; i <= a0; ++i) printf("0");
  printf("\n");
}

```