#include <bits/stdc++.h>
using namespace std;
int main() {
  int zz, zo, oz, oo;
  scanf("%d%d%d%d", &zz, &zo, &oz, &oo);
  int nz = -1, no = -1;
  for (long long i = 1; (i - 1) * i / 2 <= max(zz, oo) && i <= 1e5; i++) {
    if ((i - 1) * i / 2 == zz) nz = i;
    if ((i - 1) * i / 2 == oo) no = i;
  }
  if (nz == -1 || no == -1) return 0 * printf("Impossible\n");
  if (zo == 0 && oz == 0) {
    if (zz && oo)
      return 0 * printf("Impossible\n");
    else if (zz)
      for (int i = 1; i <= nz; i++) printf("0");
    else if (oo)
      for (int i = 1; i <= no; i++) printf("1");
    else
      printf("1");
    return 0 * printf("\n");
  }
  if (nz == 1) {
    if (!zo) {
      if (!oz)
        for (int i = 1; i <= no; i++) printf("1");
      else if (oz != no)
        return 0 * printf("Impossible\n");
      else {
        for (int i = 1; i <= no; i++) printf("1");
        return 0 * printf("0\n");
      }
      printf("\n");
    } else {
      if (zo + oz != no) return 0 * printf("Impossible\n");
      for (int i = 0; i <= no; i++) {
        if (i) printf("1");
        if (i == oz) printf("0");
      }
      printf("\n");
    }
  } else if (no == 1) {
    if (!oz) {
      if (zo != nz)
        return 0 * printf("Impossible\n");
      else
        for (int i = 1; i <= nz; i++) printf("0");
      printf("1\n");
    } else {
      if (zo + oz != nz) return 0 * printf("Impossible\n");
      for (int i = 0; i <= nz; i++) {
        if (i) printf("0");
        if (i == zo) printf("1");
      }
      printf("\n");
    }
  } else {
    if (nz * no != zo + oz) return 0 * printf("Impossible\n");
    int res = no;
    for (int i = 1; i <= no; i++) {
      while (zo >= res) printf("0"), zo -= res, nz--;
      printf("1");
      res--;
    }
    while (nz) printf("0"), nz--;
    printf("\n");
  }
  return 0;
}

### Prompt

In Cpp, your task is to solve 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 main() {
  int zz, zo, oz, oo;
  scanf("%d%d%d%d", &zz, &zo, &oz, &oo);
  int nz = -1, no = -1;
  for (long long i = 1; (i - 1) * i / 2 <= max(zz, oo) && i <= 1e5; i++) {
    if ((i - 1) * i / 2 == zz) nz = i;
    if ((i - 1) * i / 2 == oo) no = i;
  }
  if (nz == -1 || no == -1) return 0 * printf("Impossible\n");
  if (zo == 0 && oz == 0) {
    if (zz && oo)
      return 0 * printf("Impossible\n");
    else if (zz)
      for (int i = 1; i <= nz; i++) printf("0");
    else if (oo)
      for (int i = 1; i <= no; i++) printf("1");
    else
      printf("1");
    return 0 * printf("\n");
  }
  if (nz == 1) {
    if (!zo) {
      if (!oz)
        for (int i = 1; i <= no; i++) printf("1");
      else if (oz != no)
        return 0 * printf("Impossible\n");
      else {
        for (int i = 1; i <= no; i++) printf("1");
        return 0 * printf("0\n");
      }
      printf("\n");
    } else {
      if (zo + oz != no) return 0 * printf("Impossible\n");
      for (int i = 0; i <= no; i++) {
        if (i) printf("1");
        if (i == oz) printf("0");
      }
      printf("\n");
    }
  } else if (no == 1) {
    if (!oz) {
      if (zo != nz)
        return 0 * printf("Impossible\n");
      else
        for (int i = 1; i <= nz; i++) printf("0");
      printf("1\n");
    } else {
      if (zo + oz != nz) return 0 * printf("Impossible\n");
      for (int i = 0; i <= nz; i++) {
        if (i) printf("0");
        if (i == zo) printf("1");
      }
      printf("\n");
    }
  } else {
    if (nz * no != zo + oz) return 0 * printf("Impossible\n");
    int res = no;
    for (int i = 1; i <= no; i++) {
      while (zo >= res) printf("0"), zo -= res, nz--;
      printf("1");
      res--;
    }
    while (nz) printf("0"), nz--;
    printf("\n");
  }
  return 0;
}

```