#include <bits/stdc++.h>
using namespace std;
long long int a00, a01, a10, a11;
long long int ans(long long int x) { return (x * (x - 1)) / 2; }
int main() {
  scanf("%lld %lld %lld %lld", &a00, &a01, &a10, &a11);
  long long int z = -1;
  long long int o = -1;
  for (long long int i = 0; i <= 100000LL; i++) {
    if (ans(i) == a00) {
      z = i;
      break;
    }
  }
  for (long long int i = 0; i < 100000LL; i++) {
    if (ans(i) == a11) {
      o = i;
      break;
    }
  }
  if (z == -1 || o == -1) {
    printf("Impossible");
    return 0;
  }
  if (a00 == 0 && a10 == 0 && a01 == 0 && a11 == 0) {
    printf("0");
    return 0;
  }
  int f = 0;
  if ((a10 + a01) == (z * o)) {
    long long int len = z + o;
    vector<int> v;
    for (int i = 1; i <= len; i++) {
      if (o <= a01) {
        v.push_back(0);
        z--;
        a01 -= o;
      } else {
        v.push_back(1);
        o--;
        a10 -= z;
      }
    }
    for (int i = 0; i < (int)v.size(); i++) {
      printf("%d", v[i]);
    }
    return 0;
  } else {
    if (z == 0) {
      z = 1;
      if ((a01 + a10) == (z * o)) {
        long long int len = z + o;
        vector<int> v;
        for (int i = 1; i <= len; i++) {
          if (o <= a01) {
            v.push_back(0);
            z--;
            a01 -= o;
          } else {
            v.push_back(1);
            o--;
            a10 -= z;
          }
        }
        f = 1;
        for (int i = 0; i < (int)v.size(); i++) {
          printf("%d", v[i]);
        }
        return 0;
      }
      z = 0;
    }
    if (o == 0) {
      o = 1;
      if ((a01 + a10) == (z * o)) {
        long long int len = z + o;
        vector<int> v;
        for (int i = 1; i <= len; i++) {
          if (o <= a01) {
            v.push_back(0);
            z--;
            a01 -= o;
          } else {
            v.push_back(1);
            o--;
            a10 -= z;
          }
        }
        for (int i = 0; i < (int)v.size(); i++) {
          printf("%d", v[i]);
        }
        return 0;
      }
      o = 0;
    }
    if (z == 0 && o == 0) {
      z = 1;
      o = 1;
      if ((a01 + a10) == (z * o)) {
        long long int len = z + o;
        vector<int> v;
        for (int i = 1; i <= len; i++) {
          if (o <= a01) {
            v.push_back(0);
            z--;
            a01 -= o;
          } else {
            v.push_back(1);
            o--;
            a10 -= z;
          }
        }
        for (int i = 0; i < (int)v.size(); i++) {
          printf("%d", v[i]);
        }
        return 0;
      }
    }
    printf("Impossible\n");
    return 0;
  }
  return 0;
}

### Prompt

Please formulate 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 int a00, a01, a10, a11;
long long int ans(long long int x) { return (x * (x - 1)) / 2; }
int main() {
  scanf("%lld %lld %lld %lld", &a00, &a01, &a10, &a11);
  long long int z = -1;
  long long int o = -1;
  for (long long int i = 0; i <= 100000LL; i++) {
    if (ans(i) == a00) {
      z = i;
      break;
    }
  }
  for (long long int i = 0; i < 100000LL; i++) {
    if (ans(i) == a11) {
      o = i;
      break;
    }
  }
  if (z == -1 || o == -1) {
    printf("Impossible");
    return 0;
  }
  if (a00 == 0 && a10 == 0 && a01 == 0 && a11 == 0) {
    printf("0");
    return 0;
  }
  int f = 0;
  if ((a10 + a01) == (z * o)) {
    long long int len = z + o;
    vector<int> v;
    for (int i = 1; i <= len; i++) {
      if (o <= a01) {
        v.push_back(0);
        z--;
        a01 -= o;
      } else {
        v.push_back(1);
        o--;
        a10 -= z;
      }
    }
    for (int i = 0; i < (int)v.size(); i++) {
      printf("%d", v[i]);
    }
    return 0;
  } else {
    if (z == 0) {
      z = 1;
      if ((a01 + a10) == (z * o)) {
        long long int len = z + o;
        vector<int> v;
        for (int i = 1; i <= len; i++) {
          if (o <= a01) {
            v.push_back(0);
            z--;
            a01 -= o;
          } else {
            v.push_back(1);
            o--;
            a10 -= z;
          }
        }
        f = 1;
        for (int i = 0; i < (int)v.size(); i++) {
          printf("%d", v[i]);
        }
        return 0;
      }
      z = 0;
    }
    if (o == 0) {
      o = 1;
      if ((a01 + a10) == (z * o)) {
        long long int len = z + o;
        vector<int> v;
        for (int i = 1; i <= len; i++) {
          if (o <= a01) {
            v.push_back(0);
            z--;
            a01 -= o;
          } else {
            v.push_back(1);
            o--;
            a10 -= z;
          }
        }
        for (int i = 0; i < (int)v.size(); i++) {
          printf("%d", v[i]);
        }
        return 0;
      }
      o = 0;
    }
    if (z == 0 && o == 0) {
      z = 1;
      o = 1;
      if ((a01 + a10) == (z * o)) {
        long long int len = z + o;
        vector<int> v;
        for (int i = 1; i <= len; i++) {
          if (o <= a01) {
            v.push_back(0);
            z--;
            a01 -= o;
          } else {
            v.push_back(1);
            o--;
            a10 -= z;
          }
        }
        for (int i = 0; i < (int)v.size(); i++) {
          printf("%d", v[i]);
        }
        return 0;
      }
    }
    printf("Impossible\n");
    return 0;
  }
  return 0;
}

```