#include <bits/stdc++.h>
using namespace std;
const int N = 2e6 + 20;
long long a[N];
char s[N];
long long fun(long long x) { return x * (x - 1) / 2; }
int main() {
  while (cin >> a[0] >> a[1] >> a[2] >> a[3]) {
    long long sum = 0, n = 1;
    for (int i = 0; i < 4; i++) sum += a[i];
    bool flag = true;
    while (fun(n) < sum) n++;
    if (fun(n) != sum) flag = false;
    if (n == 1) {
      if (a[1] || a[2] || a[3] || a[0])
        puts("Impossible");
      else
        puts("0");
      continue;
    }
    long long zero = 0, one = 0;
    while (fun(zero) < a[0]) zero++;
    while (fun(one) < a[3]) one++;
    if (one == 0 && (a[1] || a[2])) one = 1;
    if (zero == 0 && (a[1] || a[2])) zero = 1;
    if (fun(one) != a[3] || fun(zero) != a[0] || zero + one != n) flag = false;
    if (a[1] + a[2] != one * zero) flag = false;
    if (flag == false) {
      puts("Impossible");
      continue;
    }
    int t = a[2], r = 0;
    if (zero) t = a[2] / zero, r = a[2] % zero;
    for (int i = 1; i <= t; i++) s[i] = '1';
    for (int i = t + 1; i <= t + zero; i++) s[i] = '0';
    for (int i = t + zero + 1; i <= n; i++) s[i] = '1';
    swap(s[t + zero + 1], s[t + zero + 1 - r]);
    printf("%s\n", s + 1);
  }
  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;
const int N = 2e6 + 20;
long long a[N];
char s[N];
long long fun(long long x) { return x * (x - 1) / 2; }
int main() {
  while (cin >> a[0] >> a[1] >> a[2] >> a[3]) {
    long long sum = 0, n = 1;
    for (int i = 0; i < 4; i++) sum += a[i];
    bool flag = true;
    while (fun(n) < sum) n++;
    if (fun(n) != sum) flag = false;
    if (n == 1) {
      if (a[1] || a[2] || a[3] || a[0])
        puts("Impossible");
      else
        puts("0");
      continue;
    }
    long long zero = 0, one = 0;
    while (fun(zero) < a[0]) zero++;
    while (fun(one) < a[3]) one++;
    if (one == 0 && (a[1] || a[2])) one = 1;
    if (zero == 0 && (a[1] || a[2])) zero = 1;
    if (fun(one) != a[3] || fun(zero) != a[0] || zero + one != n) flag = false;
    if (a[1] + a[2] != one * zero) flag = false;
    if (flag == false) {
      puts("Impossible");
      continue;
    }
    int t = a[2], r = 0;
    if (zero) t = a[2] / zero, r = a[2] % zero;
    for (int i = 1; i <= t; i++) s[i] = '1';
    for (int i = t + 1; i <= t + zero; i++) s[i] = '0';
    for (int i = t + zero + 1; i <= n; i++) s[i] = '1';
    swap(s[t + zero + 1], s[t + zero + 1 - r]);
    printf("%s\n", s + 1);
  }
  return 0;
}

```