Problem: While creating high loaded systems one should pay a special attention to caching. This problem will be about one of the most popular caching algorithms called LRU (Least Recently Used).

Suppose the cache may store no more than k objects. At the beginning of the workflow the cache is empty. When some object is queried we check if it is present in the cache and move it here if it's not. If there are more than k objects in the cache after this, the least recently used one should be removed. In other words, we remove the object that has the smallest time of the last query.

Consider there are n videos being stored on the server, all of the same size. Cache can store no more than k videos and caching algorithm described above is applied. We know that any time a user enters the server he pick the video i with probability pi. The choice of the video is independent to any events before.

The goal of this problem is to count for each of the videos the probability it will be present in the cache after 10100 queries.

Input

The first line of the input contains two integers n and k (1 ≤ k ≤ n ≤ 20) — the number of videos and the size of the cache respectively. Next line contains n real numbers pi (0 ≤ pi ≤ 1), each of them is given with no more than two digits after decimal point.

It's guaranteed that the sum of all pi is equal to 1.

Output

Print n real numbers, the i-th of them should be equal to the probability that the i-th video will be present in the cache after 10100 queries. You answer will be considered correct if its absolute or relative error does not exceed 10 - 6. 

Namely: let's assume that your answer is a, and the answer of the jury is b. The checker program will consider your answer correct, if <image>.

Examples

Input

3 1
0.3 0.2 0.5


Output

0.3 0.2 0.5 

Input

2 1
0.0 1.0


Output

0.0 1.0 

Input

3 2
0.3 0.2 0.5


Output

0.675 0.4857142857142857 0.8392857142857143 

Input

3 3
0.2 0.3 0.5


Output

1.0 1.0 1.0 

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
int break_point() {
  char c;
  while ((c = getchar()) != '\n')
    ;
  return 0;
}
template <typename T>
void read_integer(T &r) {
  bool sign = 0;
  r = 0;
  char c;
  while (1) {
    c = getchar();
    if (c == '-') {
      sign = 1;
      break;
    }
    if (c != ' ' && c != '\n') {
      r = c - '0';
      break;
    }
  }
  while (1) {
    c = getchar();
    if (c == ' ' || c == '\n') break;
    r = r * 10 + (c - '0');
  }
  if (sign) r = -r;
}
inline long long binpow(long long a, long long b, long long mod) {
  long long res = 1;
  while (b) {
    if (b & 1) {
      res *= a;
      res %= mod;
      b--;
    } else {
      a *= a;
      a %= mod;
      b >>= 1;
    }
  }
  return res;
}
inline long long binpow(long long a, long long b) {
  long long res = 1;
  while (b) {
    if (b & 1) {
      res *= a;
      b--;
    } else {
      a *= a;
      b >>= 1;
    }
  }
  return res;
}
inline int getbit(int x, int b) { return (x >> b) & 1; }
inline long long getbit(long long x, int b) { return (x >> b) & 1; }
inline unsigned long long getbit(unsigned long long x, int b) {
  return (x >> b) & 1;
}
inline int setbit(int x, int b) { return x | (1 << b); }
inline void _setbit(int &x, int b) { x = setbit(x, b); }
inline long long setbit(long long x, int b) { return x | (1ll << b); }
inline void _setbit(long long &x, int b) { x = setbit(x, b); }
inline int unsetbit(int x, int b) { return x & (INT_MAX - (1 << b)); }
inline void _unsetbit(int &x, int b) { x = unsetbit(x, b); }
inline int countbit(int x) {
  x = x - ((x >> 1) & 0x55555555);
  x = (x & 0x33333333) + ((x >> 2) & 0x33333333);
  return ((x + (x >> 4) & 0xF0F0F0F) * 0x1010101) >> 24;
}
inline long long countbit(long long x) {
  int p1 = (x >> 32) & ((1ll << 32) - 1);
  int p2 = x & ((1ll << 32) - 1);
  return countbit(p1) + countbit(p2);
}
template <typename T>
void printbit(T x, int len) {
  for (int i = len - 1; i >= 0; i--) printf("%d", getbit(x, i));
}
int gcd(int a, int b) { return b == 0 ? a : gcd(b, a % b); }
long long gcd(long long a, long long b) { return b == 0 ? a : gcd(b, a % b); }
template <typename A, typename B>
ostream &operator<<(ostream &stream, const pair<A, B> &p) {
  stream << "{" << p.first << "," << p.second << "}";
  return stream;
}
template <typename A>
ostream &operator<<(ostream &stream, const vector<A> &v) {
  stream << "[";
  for (auto itr = v.begin(); itr != v.end(); itr++) stream << *itr << " ";
  stream << "]";
  return stream;
}
template <typename A, typename B>
ostream &operator<<(ostream &stream, const map<A, B> &v) {
  stream << "[";
  for (auto itr = v.begin(); itr != v.end(); itr++) stream << *itr << " ";
  stream << "]";
  return stream;
}
template <typename A>
ostream &operator<<(ostream &stream, const set<A> &v) {
  stream << "[";
  for (auto itr = v.begin(); itr != v.end(); itr++) stream << *itr << " ";
  stream << "]";
  return stream;
}
template <typename A>
ostream &operator<<(ostream &stream, const stack<A> &v) {
  stack<A> st = v;
  stream << "[";
  while (!st.empty()) {
    stream << st.top() << " ";
    st.pop();
  }
  stream << "]";
  return stream;
}
template <typename A>
ostream &operator<<(ostream &stream, const priority_queue<A> &v) {
  priority_queue<A> q = v;
  stream << "[";
  while (!q.empty()) {
    stream << q.top() << " ";
    q.pop();
  }
  stream << "]";
  return stream;
}
template <typename A>
ostream &operator<<(ostream &stream, const queue<A> &v) {
  queue<A> q = v;
  stream << "[";
  while (!q.empty()) {
    stream << q.front() << " ";
    q.pop();
  }
  stream << "]";
  return stream;
}
void run();
int main() {
  srand(time(NULL));
  do {
    run();
    if (0) {
      0 ? printf("-------------------------------\n") : 0;
      0 ? printf("-------------------------------\n") : 0;
      0 ? break_point() : 0;
    }
  } while (0);
  return 0;
}
const int mod = 1e9 + 7;
const int N = 21;
double p[N];
double dp[1 << N];
double res[N];
void run() {
  int n, k;
  scanf("%d%d", &n, &k);
  int zeros = 0;
  for (int i = 0; i < n; ++i) {
    scanf("%lf", &p[i]);
    zeros += p[i] < (1e-8);
  }
  int to = 1 << n;
  dp[0] = 1.0;
  if (n - zeros < k) k = n - zeros;
  for (int i = 1; i < to; ++i) {
    bool f = true;
    double sum = 1.0;
    for (int j = 0; j < n; ++j)
      if (getbit(i, j)) sum -= p[j];
    for (int j = 0; j < n; ++j) {
      if (!getbit(i, j)) continue;
      if (p[j] < (1e-8)) {
        f = false;
        continue;
      }
      dp[i] += dp[i ^ (1 << j)] * p[j] / (sum + p[j]);
    }
    if (f && countbit(i) == k) {
      for (int j = 0; j < n; ++j) {
        if (getbit(i, j)) res[j] += dp[i];
      }
    }
    0 ? (cout << "f"
              << " = " << (f) << ","
              << "i"
              << " = " << (i) << ","
              << "dp[i]"
              << " = " << (dp[i]) << "\n")
      : cout << "";
  }
  for (int i = 0; i < n; ++i) printf("%.10lf ", res[i]);
  putchar('\n');
}