#include <bits/stdc++.h>
using namespace std;
long long a00, a01, a10, a11;
long long sum[100010];
long long calc(long long x) {
  long long l = 1, r = 1 << 20;
  while (l <= r) {
    long long mid = (l + r) >> 1;
    if (mid * (mid - 1) / 2 == x)
      return mid;
    else if (mid * (mid - 1) / 2 < x)
      l = mid + 1;
    else
      r = mid - 1;
  }
  return -1;
}
int main() {
  scanf("%lld%lld%lld%lld", &a00, &a01, &a10, &a11);
  if (!a00 && !a01 && !a10 && !a11) {
    puts("1");
    return 0;
  }
  long long n = calc(a00 + a01 + a10 + a11), t0 = calc(a00), t1 = calc(a11);
  if (n == -1 || t0 == -1 || t1 == -1) {
    puts("Impossible");
    return 0;
  }
  if (n != t1 + t0 && t1 == 1) t1--;
  if (n != t1 + t0 && t0 == 1) t0--;
  if (n != t1 + t0) {
    puts("Impossible");
    return 0;
  }
  for (int i = 1; i <= t1; i++) {
    long long tt = min(a01, t0);
    sum[tt]++;
    a01 -= tt;
  }
  for (int i = 0; i <= t0; i++) {
    if (i) putchar('0');
    while (sum[i]--) putchar('1');
  }
  puts("");
  return 0;
}

### Prompt

Please create a solution in Cpp 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 a00, a01, a10, a11;
long long sum[100010];
long long calc(long long x) {
  long long l = 1, r = 1 << 20;
  while (l <= r) {
    long long mid = (l + r) >> 1;
    if (mid * (mid - 1) / 2 == x)
      return mid;
    else if (mid * (mid - 1) / 2 < x)
      l = mid + 1;
    else
      r = mid - 1;
  }
  return -1;
}
int main() {
  scanf("%lld%lld%lld%lld", &a00, &a01, &a10, &a11);
  if (!a00 && !a01 && !a10 && !a11) {
    puts("1");
    return 0;
  }
  long long n = calc(a00 + a01 + a10 + a11), t0 = calc(a00), t1 = calc(a11);
  if (n == -1 || t0 == -1 || t1 == -1) {
    puts("Impossible");
    return 0;
  }
  if (n != t1 + t0 && t1 == 1) t1--;
  if (n != t1 + t0 && t0 == 1) t0--;
  if (n != t1 + t0) {
    puts("Impossible");
    return 0;
  }
  for (int i = 1; i <= t1; i++) {
    long long tt = min(a01, t0);
    sum[tt]++;
    a01 -= tt;
  }
  for (int i = 0; i <= t0; i++) {
    if (i) putchar('0');
    while (sum[i]--) putchar('1');
  }
  puts("");
  return 0;
}

```