#include <bits/stdc++.h>
using namespace std;
int l_0, l_1;
long long a00, a01, a10, a11, n0, n1, t, tmp;
char s[1000003];
inline bool judge(long long x, long long &num) {
  tmp = 1 + 8 * x;
  t = sqrt(0.0 + tmp);
  if (t * t != tmp) {
    return false;
  }
  num = (1 + t) >> 1;
  return true;
}
int main() {
  while (4 == scanf("%I64d%I64d%I64d%I64d", &a00, &a01, &a10, &a11)) {
    if (a00 + a01 + a10 + a11 == 0) {
      printf("0\n");
    } else if (!judge(a00, n0) || !judge(a11, n1)) {
      printf("Impossible\n");
    } else if (a00 + a01 + a10 == 0) {
      while (n1 > 0) {
        printf("1");
        --n1;
      }
      printf("\n");
    } else if (a01 + a10 + a11 == 0) {
      while (n0 > 0) {
        printf("0");
        --n0;
      }
      printf("\n");
    } else if (n0 * n1 != a01 + a10) {
      printf("Impossible\n");
    } else {
      l_0 = a01 / n1;
      l_1 = n1 - a01 % n1;
      for (int i = 0; i < l_0; ++i) {
        printf("0");
        --n0;
      }
      for (int i = 0; i < l_1; ++i) {
        printf("1");
        --n1;
      }
      if (n0 > 0) {
        printf("0");
        --n0;
      }
      while (n1 > 0) {
        printf("1");
        --n1;
      }
      while (n0 > 0) {
        printf("0");
        --n0;
      }
      printf("\n");
    }
  }
  return 0;
}

### Prompt

Please formulate 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 l_0, l_1;
long long a00, a01, a10, a11, n0, n1, t, tmp;
char s[1000003];
inline bool judge(long long x, long long &num) {
  tmp = 1 + 8 * x;
  t = sqrt(0.0 + tmp);
  if (t * t != tmp) {
    return false;
  }
  num = (1 + t) >> 1;
  return true;
}
int main() {
  while (4 == scanf("%I64d%I64d%I64d%I64d", &a00, &a01, &a10, &a11)) {
    if (a00 + a01 + a10 + a11 == 0) {
      printf("0\n");
    } else if (!judge(a00, n0) || !judge(a11, n1)) {
      printf("Impossible\n");
    } else if (a00 + a01 + a10 == 0) {
      while (n1 > 0) {
        printf("1");
        --n1;
      }
      printf("\n");
    } else if (a01 + a10 + a11 == 0) {
      while (n0 > 0) {
        printf("0");
        --n0;
      }
      printf("\n");
    } else if (n0 * n1 != a01 + a10) {
      printf("Impossible\n");
    } else {
      l_0 = a01 / n1;
      l_1 = n1 - a01 % n1;
      for (int i = 0; i < l_0; ++i) {
        printf("0");
        --n0;
      }
      for (int i = 0; i < l_1; ++i) {
        printf("1");
        --n1;
      }
      if (n0 > 0) {
        printf("0");
        --n0;
      }
      while (n1 > 0) {
        printf("1");
        --n1;
      }
      while (n0 > 0) {
        printf("0");
        --n0;
      }
      printf("\n");
    }
  }
  return 0;
}

```