Problem: Twilight Sparkle was playing Ludo with her friends Rainbow Dash, Apple Jack and Flutter Shy. But she kept losing. Having returned to the castle, Twilight Sparkle became interested in the dice that were used in the game.

The dice has m faces: the first face of the dice contains a dot, the second one contains two dots, and so on, the m-th face contains m dots. Twilight Sparkle is sure that when the dice is tossed, each face appears with probability <image>. Also she knows that each toss is independent from others. Help her to calculate the expected maximum number of dots she could get after tossing the dice n times.

Input

A single line contains two integers m and n (1 ≤ m, n ≤ 105).

Output

Output a single real number corresponding to the expected maximum. The answer will be considered correct if its relative or absolute error doesn't exceed 10  - 4.

Examples

Input

6 1


Output

3.500000000000


Input

6 3


Output

4.958333333333


Input

2 2


Output

1.750000000000

Note

Consider the third test example. If you've made two tosses:

  1. You can get 1 in the first toss, and 2 in the second. Maximum equals to 2. 
  2. You can get 1 in the first toss, and 1 in the second. Maximum equals to 1. 
  3. You can get 2 in the first toss, and 1 in the second. Maximum equals to 2. 
  4. You can get 2 in the first toss, and 2 in the second. Maximum equals to 2. 



The probability of each outcome is 0.25, that is expectation equals to: 

<image>

You can read about expectation using the following link: http://en.wikipedia.org/wiki/Expected_value

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
auto clk = clock();
const int dx[] = {0, 0, -1, 1}, dy[] = {-1, 1, 0, 0};
const int dx8[] = {-1, -1, -1, 0, 1, 1, 1, 0},
          dy8[] = {-1, 0, 1, 1, 1, 0, -1, -1};
using namespace std;
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
const long long MAXN = 100010;
long long Gcd(long long a, long long b) {
  if (a % b == 0) return b;
  return Gcd(b, a % b);
}
long long Max(long long a, long long b) {
  if (a > b) return a;
  return b;
}
long long Min(long long a, long long b) {
  if (a < b) return a;
  return b;
}
void printvector(std::vector<long long> v) {
  for (int i = 0; i < v.size(); ++i) {
    cout << v[i] << " ";
  }
  cout << "" << endl;
}
void printarray(long long a[], long long n) {
  for (long long i = 0; i < n; ++i) {
    cout << a[i] << " ";
  }
  cout << "" << endl;
}
long long findlcm(vector<long long> arr, long long n) {
  long long ans = arr[0];
  for (int i = 1; i < n; i++) ans = (((arr[i] * ans)) / (Gcd(arr[i], ans)));
  return ans;
}
long long power(long long x, long long y, long long p) {
  long long res = 1;
  x = x % p;
  while (y > 0) {
    if (y & 1) res = (res * x) % p;
    y = y >> 1;
    x = (x * x) % p;
  }
  return res;
}
long long lowerbound(long long k, vector<long long> v) {
  long long l = 0;
  long long size = v.size();
  long long r = size - 1;
  long long mid;
  while (l <= r) {
    mid = (l + r) / 2;
    if (v[mid] < k)
      l = mid + 1;
    else {
      r = mid - 1;
    }
  }
  return l;
}
long long upperbound(long long k, vector<long long> v) {
  long long l = 0;
  long long size = v.size();
  long long r = size - 1;
  long long mid;
  while (l <= r) {
    mid = (l + r) / 2;
    if (v[mid] > k)
      r = mid - 1;
    else {
      l = mid + 1;
    }
  }
  return l;
}
long long spf[MAXN];
void sieve() {
  spf[1] = 1;
  for (int i = 2; i < MAXN; i++) spf[i] = i;
  for (int i = 4; i < MAXN; i += 2) spf[i] = 2;
  for (int i = 3; i * i < MAXN; i++) {
    if (spf[i] == i) {
      for (int j = i * i; j < MAXN; j += i)
        if (spf[j] == j) spf[j] = i;
    }
  }
}
long long n, m;
vector<long long> shortPath(vector<pair<long long, long long>> v[],
                            long long src, long long V = 0) {
  set<pair<long long, long long>> setds;
  long long sizee = V;
  long long IN = LLONG_MAX;
  vector<long long> dist(sizee, IN);
  vector<bool> vis(sizee, false);
  setds.insert(make_pair(0, src));
  dist[src] = 0;
  while (!setds.empty()) {
    pair<long long, long long> tmp = *(setds.begin());
    setds.erase(setds.begin());
    long long u = tmp.second;
    if (vis[u]) continue;
    vis[u] = true;
    vector<pair<long long, long long>>::iterator i;
    for (auto i = v[u].begin(); i != v[u].end(); ++i) {
      long long v = (*i).first;
      long long weight = (*i).second;
      if (dist[v] > dist[u] + weight) {
        if (dist[v] != LLONG_MAX)
          setds.erase(setds.find(make_pair(dist[v], v)));
        dist[v] = dist[u] + weight;
        setds.insert(make_pair(dist[v], v));
      }
    }
  }
  return dist;
}
long long root(long long a[], long long r) {
  if (a[r] == r) {
    return r;
  } else {
    long long x = root(a, a[r]);
    a[r] = x;
    return x;
  }
}
void unio(long long a[], long long size[], long long x, long long y) {
  x = root(a, x);
  y = root(a, y);
  if (x == y) {
    return;
  }
  if (size[x] >= size[y]) {
    a[y] = x;
    size[x] += size[y];
  } else {
    a[x] = y;
    size[y] += size[x];
  }
}
void neuer(long long txt) {
  cin >> m >> n;
  long double nn = n;
  long double mm = m;
  long double pr = 0;
  long double ps = 0;
  for (long long i = 1; i <= m - 1; i++) {
    long double ii = i;
    long double po = ii / mm;
    long double oi = pow(po, nn);
    ps = (ps + oi);
  }
  long double x = (mm);
  x = (x - ps);
  cout << setprecision(10) << x << endl;
  return;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  long long x68 = 1;
  for (long long vi = 1; vi <= x68; vi++) {
    neuer(vi);
  }
  return 0;
}