#include <bits/stdc++.h>
const double eps = 1e-10;
const float epsf = 1e-6;
using namespace std;
inline long long int __gcd(long long int a, long long int b) {
  if (a == 0 || b == 0) {
    return max(a, b);
  }
  long long int tempa, tempb;
  while (1) {
    if (a % b == 0)
      return b;
    else {
      tempa = a;
      tempb = b;
      a = tempb;
      b = tempa % tempb;
    }
  }
}
inline int compfloat(float& x, float& y) {
  if (fabs(x - y) < epsf)
    return 0;
  else if (x - y > 0)
    return 1;
  return -1;
}
inline int compdouble(double x, double y) {
  if (fabs(x - y) < eps)
    return 0;
  else if (x - y > 0)
    return 1;
  else
    return -1;
}
bool prime(long long int k) {
  for (long long int i = 2; i * i <= k; i++)
    if (k % i == 0) {
      return false;
    }
  return true;
}
void pdash(int n = 1) {
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < 30; j++) {
      cout << "-";
    }
    cout << "\n";
  }
}
long long int power(long long int x, long long int y) {
  long long int result = 1;
  while (y > 0) {
    if (y & 1) {
      result = (result * x);
    }
    y = y >> 1;
    x = (x * x);
  }
  return result;
}
long long int power(long long int x, long long int y, long long int z) {
  long long int result = 1;
  x = x % z;
  while (y > 0) {
    if (y & 1) {
      result = (result * x) % z;
    }
    y = y >> 1;
    x = (x * x) % z;
  }
  return result;
}
long long int modInverse(long long int n, long long int p) {
  return power(n, p - 2, p);
}
long long int nCrF(long long int n, long long int r, long long int p) {
  if (r == 0) return 1;
  long long int f[n + 1];
  f[0] = 1;
  for (long long int i = 1; i <= n; i++) f[i] = f[i - 1] * i % p;
  return (f[n] * modInverse(f[r], p) % p * modInverse(f[n - r], p) % p) % p;
}
void cordinate_compression(vector<int>& v) {
  vector<int> p = v;
  sort(p.begin(), p.end());
  p.erase(unique(p.begin(), p.end()), p.end());
  for (int i = 0; i < (int)((v).size()); i++)
    v[i] = (int)(lower_bound(p.begin(), p.end(), v[i]) - p.begin());
}
void solve() {
  string str;
  long long int n = 0;
  getline(cin, str);
  string ans = "p";
  long long int pos, neg;
  pos = 1;
  neg = 0;
  for (int i = 0; i < (int)((str).size()); i += 4) {
    if (str[i + 2] == '=') {
      n = stoi(string(str.begin() + (i + 4), str.end()));
      break;
    } else {
      if (str[i + 2] == '+') {
        ans += "p";
        pos++;
      } else {
        ans += "n";
        neg++;
      }
    }
  }
  long long int lambda = (n - (pos - neg));
  vector<long long int> positive(pos, 1);
  vector<long long int> negative(neg, 1);
  if (lambda < -neg * (n - 1) or lambda > pos * (n - 1)) {
    cout << "Impossible\n";
    return;
  }
  if (lambda > 0) {
    for (int i = 0; i < (int)((positive).size()) and lambda; i++) {
      long long int a = min(lambda, n - 1);
      positive[i] += a;
      lambda -= a;
    }
  }
  if (lambda < 0) {
    lambda *= -1;
    for (int i = 0; i < (int)((negative).size()) and lambda; i++) {
      long long int a = min(lambda, n - 1);
      negative[i] += a;
      lambda -= a;
    }
  }
  cout << "Possible\n";
  cout << positive.back() << " ";
  positive.pop_back();
  ans = string(ans.begin() + 1, ans.end());
  for (int i = 0; i < (int)((ans).size()); i++) {
    if (ans[i] == 'p') {
      cout << "+ " << positive.back() << " ";
      positive.pop_back();
    } else if (ans[i] == 'n') {
      cout << "- " << negative.back() << " ";
      negative.pop_back();
    }
  }
  cout << "= " << n << "\n";
}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  int t = 1;
  while (t--) {
    solve();
  }
}

### Prompt

Please create a solution in Cpp to the following problem:

You are given a rebus of form ? + ? - ? + ? = n, consisting of only question marks, separated by arithmetic operation '+' and '-', equality and positive integer n. The goal is to replace each question mark with some positive integer from 1 to n, such that equality holds.

Input

The only line of the input contains a rebus. It's guaranteed that it contains no more than 100 question marks, integer n is positive and doesn't exceed 1 000 000, all letters and integers are separated by spaces, arithmetic operations are located only between question marks.

Output

The first line of the output should contain "Possible" (without quotes) if rebus has a solution and "Impossible" (without quotes) otherwise.

If the answer exists, the second line should contain any valid rebus with question marks replaced by integers from 1 to n. Follow the format given in the samples.

Examples

Input

? + ? - ? + ? + ? = 42


Output

Possible
9 + 13 - 39 + 28 + 31 = 42


Input

? - ? = 1


Output

Impossible


Input

? = 1000000


Output

Possible
1000000 = 1000000

### Response

```cpp
#include <bits/stdc++.h>
const double eps = 1e-10;
const float epsf = 1e-6;
using namespace std;
inline long long int __gcd(long long int a, long long int b) {
  if (a == 0 || b == 0) {
    return max(a, b);
  }
  long long int tempa, tempb;
  while (1) {
    if (a % b == 0)
      return b;
    else {
      tempa = a;
      tempb = b;
      a = tempb;
      b = tempa % tempb;
    }
  }
}
inline int compfloat(float& x, float& y) {
  if (fabs(x - y) < epsf)
    return 0;
  else if (x - y > 0)
    return 1;
  return -1;
}
inline int compdouble(double x, double y) {
  if (fabs(x - y) < eps)
    return 0;
  else if (x - y > 0)
    return 1;
  else
    return -1;
}
bool prime(long long int k) {
  for (long long int i = 2; i * i <= k; i++)
    if (k % i == 0) {
      return false;
    }
  return true;
}
void pdash(int n = 1) {
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < 30; j++) {
      cout << "-";
    }
    cout << "\n";
  }
}
long long int power(long long int x, long long int y) {
  long long int result = 1;
  while (y > 0) {
    if (y & 1) {
      result = (result * x);
    }
    y = y >> 1;
    x = (x * x);
  }
  return result;
}
long long int power(long long int x, long long int y, long long int z) {
  long long int result = 1;
  x = x % z;
  while (y > 0) {
    if (y & 1) {
      result = (result * x) % z;
    }
    y = y >> 1;
    x = (x * x) % z;
  }
  return result;
}
long long int modInverse(long long int n, long long int p) {
  return power(n, p - 2, p);
}
long long int nCrF(long long int n, long long int r, long long int p) {
  if (r == 0) return 1;
  long long int f[n + 1];
  f[0] = 1;
  for (long long int i = 1; i <= n; i++) f[i] = f[i - 1] * i % p;
  return (f[n] * modInverse(f[r], p) % p * modInverse(f[n - r], p) % p) % p;
}
void cordinate_compression(vector<int>& v) {
  vector<int> p = v;
  sort(p.begin(), p.end());
  p.erase(unique(p.begin(), p.end()), p.end());
  for (int i = 0; i < (int)((v).size()); i++)
    v[i] = (int)(lower_bound(p.begin(), p.end(), v[i]) - p.begin());
}
void solve() {
  string str;
  long long int n = 0;
  getline(cin, str);
  string ans = "p";
  long long int pos, neg;
  pos = 1;
  neg = 0;
  for (int i = 0; i < (int)((str).size()); i += 4) {
    if (str[i + 2] == '=') {
      n = stoi(string(str.begin() + (i + 4), str.end()));
      break;
    } else {
      if (str[i + 2] == '+') {
        ans += "p";
        pos++;
      } else {
        ans += "n";
        neg++;
      }
    }
  }
  long long int lambda = (n - (pos - neg));
  vector<long long int> positive(pos, 1);
  vector<long long int> negative(neg, 1);
  if (lambda < -neg * (n - 1) or lambda > pos * (n - 1)) {
    cout << "Impossible\n";
    return;
  }
  if (lambda > 0) {
    for (int i = 0; i < (int)((positive).size()) and lambda; i++) {
      long long int a = min(lambda, n - 1);
      positive[i] += a;
      lambda -= a;
    }
  }
  if (lambda < 0) {
    lambda *= -1;
    for (int i = 0; i < (int)((negative).size()) and lambda; i++) {
      long long int a = min(lambda, n - 1);
      negative[i] += a;
      lambda -= a;
    }
  }
  cout << "Possible\n";
  cout << positive.back() << " ";
  positive.pop_back();
  ans = string(ans.begin() + 1, ans.end());
  for (int i = 0; i < (int)((ans).size()); i++) {
    if (ans[i] == 'p') {
      cout << "+ " << positive.back() << " ";
      positive.pop_back();
    } else if (ans[i] == 'n') {
      cout << "- " << negative.back() << " ";
      negative.pop_back();
    }
  }
  cout << "= " << n << "\n";
}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  int t = 1;
  while (t--) {
    solve();
  }
}

```