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
#include <bits/stdc++.h>
using namespace std;
int II() {
  int q;
  scanf("%d", &q);
  return q;
}
long long LII() {
  long long q;
  scanf("%lld", &q);
  return q;
}
long long search(long long baki, long long sum, long long mot, long long N) {
  long long l = 1, r = N;
  long long re = 1;
  while (l <= r) {
    long long mid = (l + r) / 2;
    if ((sum + mid + baki) <= mot) {
      re = mid;
      l = mid + 1;
    } else
      r = mid - 1;
  }
  return re;
}
long long search_neg(long long baki, long long neg_sum, long long pos_sum,
                     long long N) {
  long long l = 1, r = N, re = 1;
  while (l <= r) {
    long long mid = (l + r) / 2;
    if ((neg_sum + mid + baki) <= (pos_sum - N)) {
      re = mid;
      l = mid + 1;
    } else
      r = mid - 1;
  }
  return re;
}
void solve() {
  long long pos = 0, neg = 0;
  vector<char> v;
  long long N;
  v.push_back('+');
  while (1) {
    char c1, c2;
    cin >> c1 >> c2;
    if (c2 == '=') {
      cin >> N;
      break;
    }
    v.push_back(c2);
  }
  for (auto it : v) {
    if (it == '+')
      pos++;
    else
      neg++;
  }
  if ((((pos * N) - neg) < N) or (pos - (N * neg)) > N) {
    cout << "Impossible" << endl;
    return;
  }
  long long mot = N + neg;
  vector<long long> v1;
  long long sum = 0;
  for (long long i = 1; i <= pos; i++) {
    long long q = search(pos - i, sum, mot, N);
    sum += q;
    v1.push_back(q);
  }
  long long neg_sum = 0;
  vector<long long> v2;
  for (long long i = 1; i <= neg; i++) {
    long long q = search_neg(neg - i, neg_sum, sum, N);
    neg_sum += q;
    v2.push_back(q);
  }
  if ((sum - neg_sum) != N) {
    cout << "Impossible" << endl;
    return;
  }
  long long w1 = 0, w2 = 0;
  cout << "Possible" << endl;
  for (long long i = 0; i < v.size(); i++) {
    if (v[i] == '+') {
      if (i == 0) {
        cout << v1.back() << " ";
      } else {
        cout << "+ " << v1.back() << " ";
      }
      w1 += v1.back();
      v1.pop_back();
    } else {
      cout << "- " << v2.back() << " ";
      w2 += v2.back();
      v2.pop_back();
    }
  }
  cout << "= " << N << endl;
}
int32_t main() {
  long long tt;
  tt = 1;
  while (tt--) {
    solve();
  }
}
