#include <bits/stdc++.h>
using namespace std;
const double PI = acos(-1);
const double eps = 1e-9;
const int inf = 2000000000;
const long long infLL = 9000000000000000000;
inline bool checkBit(long long n, int i) { return n & (1LL << i); }
inline long long setBit(long long n, int i) {
  return n | (1LL << i);
  ;
}
inline long long resetBit(long long n, int i) { return n & (~(1LL << i)); }
int dx[] = {0, 0, +1, -1};
int dy[] = {+1, -1, 0, 0};
inline bool EQ(double a, double b) { return fabs(a - b) < 1e-9; }
inline bool isLeapYear(long long year) {
  return (year % 400 == 0) || (year % 4 == 0 && year % 100 != 0);
}
inline void normal(long long &a) {
  a %= 1000000007;
  (a < 0) && (a += 1000000007);
}
inline long long modMul(long long a, long long b) {
  a %= 1000000007, b %= 1000000007;
  normal(a), normal(b);
  return (a * b) % 1000000007;
}
inline long long modAdd(long long a, long long b) {
  a %= 1000000007, b %= 1000000007;
  normal(a), normal(b);
  return (a + b) % 1000000007;
}
inline long long modSub(long long a, long long b) {
  a %= 1000000007, b %= 1000000007;
  normal(a), normal(b);
  a -= b;
  normal(a);
  return a;
}
inline long long modPow(long long b, long long p) {
  long long r = 1;
  while (p) {
    if (p & 1) r = modMul(r, b);
    b = modMul(b, b);
    p >>= 1;
  }
  return r;
}
inline long long modInverse(long long a) { return modPow(a, 1000000007 - 2); }
inline long long modDiv(long long a, long long b) {
  return modMul(a, modInverse(b));
}
int main() {
  string s;
  getline(cin, s);
  int l = s.length();
  int pos = 1, neg = 0, ques = 0, n = 0;
  for (int i = 0; i < l; ++i) {
    if (s[i] == '+')
      ++pos;
    else if (s[i] == '-')
      ++neg;
    else if (s[i] == '?')
      ++ques;
    else if (s[i] == '=') {
      i += 2;
      while (i < l) {
        n *= 10;
        n += s[i] - '0';
        ++i;
      }
    }
  }
  if (!(pos - n * neg <= n && n <= n * pos - neg)) {
    ;
    cout << "Impossible";
    return 0;
  }
  cout << "Possible" << '\n';
  int sum = 0, sign;
  for (int i = 0; i < l; ++i) {
    if (s[i] == '=') {
      cout << "= " << n;
      break;
    }
    if (i == 0) {
      --pos;
      for (int j = 1; j <= n; ++j) {
        if (sum + j + pos - n * neg <= n && n <= sum + j + n * pos - neg) {
          sum += j;
          cout << j << " ";
          break;
        }
      }
    } else if (s[i] != '?') {
      if (s[i] == '+') {
        sign = 1;
        --pos;
        cout << "+"
             << " ";
      } else if (s[i] == '-') {
        sign = -1;
        --neg;
        cout << "- ";
      }
    } else if (s[i] == '?') {
      for (int j = 1; j <= n; ++j) {
        if (sum + sign * j + pos - n * neg <= n &&
            n <= sum + sign * j + n * pos - neg) {
          sum += sign * j;
          cout << j << " ";
          break;
        }
      }
    }
  }
}

### Prompt

Please provide a cpp coded solution 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 double PI = acos(-1);
const double eps = 1e-9;
const int inf = 2000000000;
const long long infLL = 9000000000000000000;
inline bool checkBit(long long n, int i) { return n & (1LL << i); }
inline long long setBit(long long n, int i) {
  return n | (1LL << i);
  ;
}
inline long long resetBit(long long n, int i) { return n & (~(1LL << i)); }
int dx[] = {0, 0, +1, -1};
int dy[] = {+1, -1, 0, 0};
inline bool EQ(double a, double b) { return fabs(a - b) < 1e-9; }
inline bool isLeapYear(long long year) {
  return (year % 400 == 0) || (year % 4 == 0 && year % 100 != 0);
}
inline void normal(long long &a) {
  a %= 1000000007;
  (a < 0) && (a += 1000000007);
}
inline long long modMul(long long a, long long b) {
  a %= 1000000007, b %= 1000000007;
  normal(a), normal(b);
  return (a * b) % 1000000007;
}
inline long long modAdd(long long a, long long b) {
  a %= 1000000007, b %= 1000000007;
  normal(a), normal(b);
  return (a + b) % 1000000007;
}
inline long long modSub(long long a, long long b) {
  a %= 1000000007, b %= 1000000007;
  normal(a), normal(b);
  a -= b;
  normal(a);
  return a;
}
inline long long modPow(long long b, long long p) {
  long long r = 1;
  while (p) {
    if (p & 1) r = modMul(r, b);
    b = modMul(b, b);
    p >>= 1;
  }
  return r;
}
inline long long modInverse(long long a) { return modPow(a, 1000000007 - 2); }
inline long long modDiv(long long a, long long b) {
  return modMul(a, modInverse(b));
}
int main() {
  string s;
  getline(cin, s);
  int l = s.length();
  int pos = 1, neg = 0, ques = 0, n = 0;
  for (int i = 0; i < l; ++i) {
    if (s[i] == '+')
      ++pos;
    else if (s[i] == '-')
      ++neg;
    else if (s[i] == '?')
      ++ques;
    else if (s[i] == '=') {
      i += 2;
      while (i < l) {
        n *= 10;
        n += s[i] - '0';
        ++i;
      }
    }
  }
  if (!(pos - n * neg <= n && n <= n * pos - neg)) {
    ;
    cout << "Impossible";
    return 0;
  }
  cout << "Possible" << '\n';
  int sum = 0, sign;
  for (int i = 0; i < l; ++i) {
    if (s[i] == '=') {
      cout << "= " << n;
      break;
    }
    if (i == 0) {
      --pos;
      for (int j = 1; j <= n; ++j) {
        if (sum + j + pos - n * neg <= n && n <= sum + j + n * pos - neg) {
          sum += j;
          cout << j << " ";
          break;
        }
      }
    } else if (s[i] != '?') {
      if (s[i] == '+') {
        sign = 1;
        --pos;
        cout << "+"
             << " ";
      } else if (s[i] == '-') {
        sign = -1;
        --neg;
        cout << "- ";
      }
    } else if (s[i] == '?') {
      for (int j = 1; j <= n; ++j) {
        if (sum + sign * j + pos - n * neg <= n &&
            n <= sum + sign * j + n * pos - neg) {
          sum += sign * j;
          cout << j << " ";
          break;
        }
      }
    }
  }
}

```