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>
using namespace std;
FILE* _fin = stdin;
FILE* _fout = stdout;
int _min(int a, int b) { return a <= b ? a : b; }
int _min(long long a, long long b) { return a <= b ? a : b; }
int _max(int a, int b) { return a >= b ? a : b; }
long long _max(long long a, long long b) { return a >= b ? a : b; }
void zero(int* data, int n) { memset(data, 0, sizeof(int) * n); }
void zero(long long* data, int n) { memset(data, 0, sizeof(long long) * n); }
void zero(char* data, int n) { memset(data, 0, sizeof(char) * n); }
char readc() {
  char var;
  fscanf(_fin, "%c", &var);
  return var;
}
int readi() {
  int var;
  fscanf(_fin, "%d", &var);
  return var;
}
double readlf() {
  double var;
  fscanf(_fin, "%lf", &var);
  return var;
}
long long readll() {
  long long var;
  fscanf(_fin, "%lld", &var);
  return var;
}
void repread(int* data, int n) {
  for (int i = 0; i < n; ++i) data[i] = readi();
}
void repread(long long* data, int n) {
  for (int i = 0; i < n; ++i) data[i] = readll();
}
int reads(char* str, int maxsize) {
  for (;;) {
    if (fgets(str, maxsize, _fin) == NULL) break;
    if (str[0] != '\n' && str[0] != '\r') break;
  }
  int slen = strlen(str);
  if (slen == 0) return 0;
  if (str[slen - 1] == '\n' || str[slen - 1] == '\r') str[--slen] = 0;
  return slen;
}
long long gcd(long long a, long long b) {
  if (b == 0) return a;
  return gcd(b, a % b);
}
long long lcm(long long a, long long b) {
  long long g = gcd(a, b);
  return (a / g) * b;
}
void reverse(char* data, int n) {
  int k = n >> 1;
  for (int i = 0; i < k; ++i) {
    char tmp = data[i];
    data[i] = data[n - i - 1];
    data[n - i - 1] = tmp;
  }
}
void reverse(int* data, int n) {
  int k = n >> 1;
  for (int i = 0; i < k; ++i) {
    int tmp = data[i];
    data[i] = data[n - i - 1];
    data[n - i - 1] = tmp;
  }
}
void reverse(long long* data, int n) {
  int k = n >> 1;
  for (int i = 0; i < k; ++i) {
    long long tmp = data[i];
    data[i] = data[n - i - 1];
    data[n - i - 1] = tmp;
  }
}
struct Veci {
  int* data;
  int size;
  int n;
};
void init(Veci* t, int size) {
  t->data = (int*)malloc(sizeof(int) * size);
  t->size = size;
  t->n = 0;
}
void resize(Veci* t) {
  int ns = t->size * 1.2f;
  t->data = (int*)realloc(t->data, sizeof(int) * ns);
  t->size = ns;
}
void add(Veci* t, int val) {
  if (t->n >= t->size) resize(t);
  int k = t->n;
  t->data[k] = val;
  t->n = k + 1;
}
void free(Veci* t) { free(t->data); }
struct Vecll {
  long long* data;
  int size;
  int n;
};
void init(Vecll* t, int size) {
  t->data = (long long*)malloc(sizeof(long long) * size);
  t->size = size;
  t->n = 0;
}
void resize(Vecll* t) {
  int ns = t->size * 1.2f;
  t->data = (long long*)realloc(t->data, sizeof(long long) * ns);
  t->size = ns;
}
void add(Vecll* t, long long val) {
  if (t->n >= t->size) resize(t);
  int k = t->n;
  t->data[k] = val;
  t->n = k + 1;
}
void free(Vecll* t) { free(t->data); }
struct Vecs {
  char** data;
  int size;
  int n;
};
void init(Vecs* t, int size) {
  t->data = (char**)malloc(sizeof(char*) * size);
  t->size = size;
  t->n = 0;
}
void resize(Vecs* t) {
  int ns = t->size * 1.2f;
  t->data = (char**)realloc(t->data, sizeof(char*) * ns);
  t->size = ns;
}
void add(Vecs* t, char* val) {
  if (t->n >= t->size) resize(t);
  int k = t->n;
  t->data[k] = val;
  t->n = k + 1;
}
void free(Vecs* t) { free(t->data); }
int ispali(int* a, int* b, int n) {
  for (int i = 0; i < n; ++i) {
    if (a[i] != b[n - i - 1]) {
      return 0;
    }
  }
  return 1;
}
int ispalc(char* a, char* b, int n) {
  for (int i = 0; i < n; ++i) {
    if (a[i] != b[n - i - 1]) {
      return 0;
    }
  }
  return 1;
}
struct Pairi {
  int x, y;
};
int cmp_Pairi(const void* _a, const void* _b) {
  Pairi* a = (Pairi*)_a;
  Pairi* b = (Pairi*)_b;
  if (a->x < b->x)
    return -1;
  else {
    if (a->x == b->x) {
      if (a->y == b->y) return 0;
      if (a->y < b->y)
        return -1;
      else
        return 1;
    } else {
      return 1;
    }
  }
}
void sort_Pairi(Pairi* d, int n) { qsort(d, n, sizeof(Pairi), cmp_Pairi); }
int cmp_Str(const void* _a, const void* _b) {
  char* a = *((char**)_a);
  char* b = *((char**)_b);
  return strcmp(a, b);
}
void sort_Str(char** str, int n) { qsort(str, n, sizeof(char*), cmp_Str); }
long long expmod(long long x, long long n, long long m) {
  long long ans = 1;
  for (; n;) {
    if (n & 1) ans = (ans * x) % m;
    x = (x * x) % m;
    n >>= 1;
  }
  return ans;
}
long long combmod(long long n, long long k, long long m) {
  long long ret = 1;
  long long div = 1;
  for (long long i = 0; i < k; ++i) {
    ret = (ret * (n - i) % m) % m;
    div = (div * (i + 1)) % m;
  }
  div = expmod(div, m - 2, m) % m;
  return (ret * div) % m;
}
int next_perm(int* data, int n) {
  int rootidx = -1;
  for (int i = n - 2; i >= 0; --i) {
    if (data[i] < data[i + 1]) {
      rootidx = i;
      break;
    }
  }
  if (rootidx == -1) return 0;
  int ceilingidx = rootidx + 1;
  for (int i = rootidx + 2; i < n; ++i) {
    if (data[i] > data[rootidx] && data[i] < data[ceilingidx]) {
      ceilingidx = i;
    }
  }
  {
    int t = data[rootidx];
    data[rootidx] = data[ceilingidx];
    data[ceilingidx] = t;
  };
  std::sort(&data[rootidx + 1], &data[rootidx + 1] + n - rootidx - 1);
  return 1;
}
int count_digits(long long a) {
  int k = 0;
  for (;;) {
    if (a == 0) break;
    k++;
    a /= 10;
  }
  return k;
}
int bs_exists(int* data, int n, int val) {
  int left = 0;
  int right = n - 1;
  for (; left < right;) {
    int mid = (left + right + 1) >> 1;
    if (data[mid] <= val)
      left = mid;
    else
      right = mid - 1;
  }
  return right;
}
double simple_factorial(int x) {
  double f = 1.0;
  for (int i = 0; i < x; ++i) {
    f *= (i + 1);
  }
  return f;
}
const long long MOD = 1e9 + 7;
int find(int* a, int n, int what) {
  int left = 0;
  int right = n - 1;
  for (; left < right;) {
    int mid = (left + right + 1) >> 1;
    if (a[mid] <= what)
      left = mid;
    else
      right = mid - 1;
  }
  return right;
}
int main() {
  {
    _fin = fopen("input.txt", "r");
    if (_fin == NULL) _fin = stdin;
  };
  int n = readi();
  int k = readi();
  double sum = 0.0;
  for (int x = 1; x <= n; ++x) {
    sum += x * (pow((double)x / n, k) - pow((double)(x - 1) / n, k));
  }
  double ans = sum;
  printf("%.12f\n", ans);
  return 0;
}