#include <bits/stdc++.h>
using namespace std;
const long long INF = (long long)LLONG_MAX;
int dx[4] = {0, -1, 0, 1};
int dy[4] = {1, 0, -1, 0};
int dx8[9] = {1, 0, -1, 0, 1, -1, -1, 1, 0};
int dy8[9] = {0, 1, 0, -1, 1, -1, 1, -1, 0};
long long ipow(long long base, long long exp) {
  long long result = 1;
  while (exp) {
    if (exp & 1) result *= base;
    exp >>= 1;
    base *= base;
  }
  return result;
}
string tos(long long n) {
  stringstream ss;
  string ans;
  ss << n;
  ss >> ans;
  return ans;
}
long long toll(string n) { return atoll(n.c_str()); }
double dist(double x1, double y1, double x2, double y2) {
  return sqrt(((x1 - x2) * (x1 - x2)) + ((y1 - y2) * (y1 - y2)));
}
int doubleCompare(double x, double y) {
  if (fabs(x - y) <= 1e-18) return 0;
  if (x < y) return -1;
  return 1;
}
int main() {
  vector<long long> ans;
  char tmp;
  long long ret = 1;
  while (1) {
    cin >> tmp;
    if (tmp == '=') break;
    if (tmp == '-') {
      ret--;
      ans.push_back(-1);
    } else if (tmp == '+') {
      ret++;
      ans.push_back(-2);
    } else {
      ans.push_back(1);
    }
  }
  long long n;
  cin >> n;
  for (int i = ans.size() - 1; i >= 0; i -= 2) {
    if (ret == n) break;
    if (i == 0) {
      while (ret < n && ans[i] < n) {
        ret++;
        ans[i]++;
      }
    } else {
      while (ret > n && ans[i - 1] == -1 && ans[i] < n) {
        ret--;
        ans[i]++;
      }
      while (ret < n && ans[i - 1] == -2 && ans[i] < n) {
        ret++;
        ans[i]++;
      }
    }
  }
  if (ret == n) {
    cout << "Possible\n";
    for (int i = 0; i < ans.size(); i++) {
      if (ans[i] == -1)
        cout << " - ";
      else if (ans[i] == -2)
        cout << " + ";
      else
        cout << ans[i];
    }
    cout << " = " << n;
  } else {
    cout << "Impossible";
  }
}

### Prompt

Develop a solution in Cpp to the problem described below:

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>
using namespace std;
const long long INF = (long long)LLONG_MAX;
int dx[4] = {0, -1, 0, 1};
int dy[4] = {1, 0, -1, 0};
int dx8[9] = {1, 0, -1, 0, 1, -1, -1, 1, 0};
int dy8[9] = {0, 1, 0, -1, 1, -1, 1, -1, 0};
long long ipow(long long base, long long exp) {
  long long result = 1;
  while (exp) {
    if (exp & 1) result *= base;
    exp >>= 1;
    base *= base;
  }
  return result;
}
string tos(long long n) {
  stringstream ss;
  string ans;
  ss << n;
  ss >> ans;
  return ans;
}
long long toll(string n) { return atoll(n.c_str()); }
double dist(double x1, double y1, double x2, double y2) {
  return sqrt(((x1 - x2) * (x1 - x2)) + ((y1 - y2) * (y1 - y2)));
}
int doubleCompare(double x, double y) {
  if (fabs(x - y) <= 1e-18) return 0;
  if (x < y) return -1;
  return 1;
}
int main() {
  vector<long long> ans;
  char tmp;
  long long ret = 1;
  while (1) {
    cin >> tmp;
    if (tmp == '=') break;
    if (tmp == '-') {
      ret--;
      ans.push_back(-1);
    } else if (tmp == '+') {
      ret++;
      ans.push_back(-2);
    } else {
      ans.push_back(1);
    }
  }
  long long n;
  cin >> n;
  for (int i = ans.size() - 1; i >= 0; i -= 2) {
    if (ret == n) break;
    if (i == 0) {
      while (ret < n && ans[i] < n) {
        ret++;
        ans[i]++;
      }
    } else {
      while (ret > n && ans[i - 1] == -1 && ans[i] < n) {
        ret--;
        ans[i]++;
      }
      while (ret < n && ans[i - 1] == -2 && ans[i] < n) {
        ret++;
        ans[i]++;
      }
    }
  }
  if (ret == n) {
    cout << "Possible\n";
    for (int i = 0; i < ans.size(); i++) {
      if (ans[i] == -1)
        cout << " - ";
      else if (ans[i] == -2)
        cout << " + ";
      else
        cout << ans[i];
    }
    cout << " = " << n;
  } else {
    cout << "Impossible";
  }
}

```