#include <bits/stdc++.h>
using namespace std;
long long zz, zo, oz, oo;
void init() { cin >> zz >> zo >> oz >> oo; }
vector<long long> pt;
void process() {
  if (zz == 0 && zo == 0 && oz == 0 && oo == 0) {
    puts("1");
    return;
  }
  for (long long i = 0; i <= 1000000; i++) {
    pt.push_back(i * (i - 1) / 2);
  }
  if (find(pt.begin(), pt.end(), zz) == pt.end() ||
      find(pt.begin(), pt.end(), oo) == pt.end()) {
    puts("Impossible");
    return;
  }
  long long nz = find(pt.begin(), pt.end(), zz) - pt.begin();
  long long no = find(pt.begin(), pt.end(), oo) - pt.begin();
  if (nz <= 1) {
    nz = (oz + zo != 0) ? 1 : 0;
  }
  if (no <= 1) {
    no = (oz + zo != 0) ? 1 : 0;
  }
  if (zo + oz != no * nz) {
    puts("Impossible");
    return;
  }
  vector<char> ans;
  while (no != 0 || nz != 0) {
    if (oz >= nz)
      ans.push_back('1'), oz -= nz, no--;
    else
      ans.push_back('0'), nz--;
  }
  for (char xx : ans) putchar(xx);
  puts("");
}
int main() {
  init();
  process();
  return 0;
}

### Prompt

Your challenge is to write 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;
long long zz, zo, oz, oo;
void init() { cin >> zz >> zo >> oz >> oo; }
vector<long long> pt;
void process() {
  if (zz == 0 && zo == 0 && oz == 0 && oo == 0) {
    puts("1");
    return;
  }
  for (long long i = 0; i <= 1000000; i++) {
    pt.push_back(i * (i - 1) / 2);
  }
  if (find(pt.begin(), pt.end(), zz) == pt.end() ||
      find(pt.begin(), pt.end(), oo) == pt.end()) {
    puts("Impossible");
    return;
  }
  long long nz = find(pt.begin(), pt.end(), zz) - pt.begin();
  long long no = find(pt.begin(), pt.end(), oo) - pt.begin();
  if (nz <= 1) {
    nz = (oz + zo != 0) ? 1 : 0;
  }
  if (no <= 1) {
    no = (oz + zo != 0) ? 1 : 0;
  }
  if (zo + oz != no * nz) {
    puts("Impossible");
    return;
  }
  vector<char> ans;
  while (no != 0 || nz != 0) {
    if (oz >= nz)
      ans.push_back('1'), oz -= nz, no--;
    else
      ans.push_back('0'), nz--;
  }
  for (char xx : ans) putchar(xx);
  puts("");
}
int main() {
  init();
  process();
  return 0;
}

```