#include <bits/stdc++.h>
using namespace std;
int main() {
  int A, B, C, D;
  scanf("%d %d %d %d", &A, &B, &C, &D);
  if (A == 0 && B == 0 && C == 0) {
    long long int z = 1;
    while (z * (z - 1) / 2LL < D) z++;
    if (z * (z - 1) / 2LL == D) {
      for (int i = 0; i < z; i++) printf("1");
      puts("");
    } else
      puts("Impossible");
    return 0;
  }
  if (D == 0 && B == 0 && C == 0) {
    long long int z = 1;
    while (z * (z - 1) / 2LL < A) z++;
    if (z * (z - 1) / 2LL == A) {
      for (int i = 0; i < z; i++) printf("0");
      puts("");
    } else
      puts("Impossible");
    return 0;
  }
  long long int x = 1, y = 1;
  while (x * (x - 1) / 2LL < A) x++;
  while (y * (y - 1) / 2LL < D) y++;
  if (x * (x - 1) / 2LL != A || y * (y - 1) / 2LL != D || B + C != x * y) {
    puts("Impossible");
    return 0;
  }
  string ret = "";
  while (x > 0 || y > 0) {
    if (x > 0 && B >= y) {
      ret += "0";
      x--;
      B -= y;
    } else {
      ret += "1";
      y--;
      C -= x;
    }
  }
  printf("%s\n", ret.c_str());
  return 0;
}

### Prompt

Generate 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 main() {
  int A, B, C, D;
  scanf("%d %d %d %d", &A, &B, &C, &D);
  if (A == 0 && B == 0 && C == 0) {
    long long int z = 1;
    while (z * (z - 1) / 2LL < D) z++;
    if (z * (z - 1) / 2LL == D) {
      for (int i = 0; i < z; i++) printf("1");
      puts("");
    } else
      puts("Impossible");
    return 0;
  }
  if (D == 0 && B == 0 && C == 0) {
    long long int z = 1;
    while (z * (z - 1) / 2LL < A) z++;
    if (z * (z - 1) / 2LL == A) {
      for (int i = 0; i < z; i++) printf("0");
      puts("");
    } else
      puts("Impossible");
    return 0;
  }
  long long int x = 1, y = 1;
  while (x * (x - 1) / 2LL < A) x++;
  while (y * (y - 1) / 2LL < D) y++;
  if (x * (x - 1) / 2LL != A || y * (y - 1) / 2LL != D || B + C != x * y) {
    puts("Impossible");
    return 0;
  }
  string ret = "";
  while (x > 0 || y > 0) {
    if (x > 0 && B >= y) {
      ret += "0";
      x--;
      B -= y;
    } else {
      ret += "1";
      y--;
      C -= x;
    }
  }
  printf("%s\n", ret.c_str());
  return 0;
}

```