Problem:
Score : 300 points

Problem Statement

In some other world, today is Christmas Eve.

There are N trees planted in Mr. Takaha's garden. The height of the i-th tree (1 \leq i \leq N) is h_i meters.

He decides to choose K trees from these trees and decorate them with electric lights. To make the scenery more beautiful, the heights of the decorated trees should be as close to each other as possible.

More specifically, let the height of the tallest decorated tree be h_{max} meters, and the height of the shortest decorated tree be h_{min} meters. The smaller the value h_{max} - h_{min} is, the better. What is the minimum possible value of h_{max} - h_{min}?

Constraints

2 \leq K < N \leq 10^5

1 \leq h_i \leq 10^9

h_i is an integer.

Input

Input is given from Standard Input in the following format:

N K
h_1
h_2
:
h_N

Output

Print the minimum possible value of h_{max} - h_{min}.

Sample Input 1

5 3
10
15
11
14
12

Sample Output 1

2

If we decorate the first, third and fifth trees, h_{max} = 12, h_{min} = 10 so h_{max} - h_{min} = 2. This is optimal.

Sample Input 2

5 3
5
7
5
7
7

Sample Output 2

0

If we decorate the second, fourth and fifth trees, h_{max} = 7, h_{min} = 7 so h_{max} - h_{min} = 0. This is optimal.

There are not too many trees in these sample inputs, but note that there can be at most one hundred thousand trees (we just can't put a sample with a hundred thousand lines here).

Solution in C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <algorithm>
#include <array>
#include <bitset>
#include <complex>
#include <functional>
#include <iomanip>
#include <iostream>
#include <map>
#include <numeric>
#include <set>
#include <stack>
#include <unordered_map>
#include <unordered_set>
#include <queue>

using namespace std;

struct BoolName : numpunct<char> {
  string t, f;
  BoolName (string t = "Yes", string f = "No") : t(t), f(f) {}
  string do_truename() const {return t;}
  string do_falsename() const {return f;}
};

struct Initializer {
  Initializer() {
    cin.tie(0);
    ios::sync_with_stdio(0);
    cout << fixed << setprecision(15) << boolalpha;
    cout.imbue(locale(cout.getloc(), new BoolName));
  }
} initializer;

template<typename T> istream& operator>>(istream &s, vector<T> &v) {
  for (T &t : v) s >> t;
  return s;
}

template<typename T> ostream& operator<<(ostream &s, const vector<T> &v) {
  for (const T &t : v) s << t << endl;
  return s;
}

void set_bool_name(string t, string f) {
  cout.imbue(locale(cout.getloc(), new BoolName(t, f)));
}

template<typename T> bool chmin(T& a, T b) {return a > b ? a = b, true : false;}

template<typename T> bool chmax(T& a, T b) {return a < b ? a = b, true : false;}

template<typename T> T min(const vector<T>& v) {return *min_element(v.begin(), v.end());}

template<typename T> T max(const vector<T>& v) {return *max_element(v.begin(), v.end());}

template<typename T> int min_element(vector<T>& v) {return min_element(v.begin(), v.end()) - v.begin();}

template<typename T> int max_element(vector<T>& v) {return max_element(v.begin(), v.end()) - v.begin();}

template<typename T> void sort(vector<T>& v) {sort(v.begin(), v.end());}

template<typename T, typename Function> void sort(vector<T>& v, Function func) {sort(v.begin(), v.end(), func);}

template<typename T> void rsort(vector<T>& v) {sort(v.rbegin(), v.rend());}

template<typename T> void reverse(vector<T>& v) {reverse(v.begin(), v.end());}

template<typename T> void unique(vector<T>& v) {v.erase(unique(v.begin(), v.end()), v.end());}

template<typename T> void nth_element(vector<T>& v, int n) {nth_element(v.begin(), v.begin() + n, v.end());}

template<typename T> bool next_permutation(vector<T>& v) {return next_permutation(v.begin(), v.end());}

template<typename T> int find(vector<T>& v, T t) {return find(v.begin(), v.end(), t) - v.begin();}

template<typename T> int in(vector<T> v, T t) {return find(v, t) != int(v.size());}

template<typename T> int lower_bound(vector<T>& v, T t) {return lower_bound(v.begin(), v.end(), t) - v.begin();}

template<typename T> int upper_bound(vector<T>& v, T t) {return upper_bound(v.begin(), v.end(), t) - v.begin();}

template<typename T> T accumulate(const vector<T>& v, function<T(T, T)> func = plus<T>()) {return accumulate(v.begin(), v.end(), T(), func);}

template<typename T> void adjacent_difference(vector<T>& v) {adjacent_difference(v.begin(), v.end(), v.begin());}

template<typename T> void adjacent_difference(vector<T>& v, vector<T>& u) {adjacent_difference(v.begin(), v.end(), u.begin());}

template<typename T> void partial_sum(vector<T>& v, vector<T>& u) {partial_sum(v.begin(), v.end(), u.begin());}

template<typename T> T inner_product(vector<T>& v, vector<T>& u) {return inner_product(v.begin(), v.end(), u.begin(), T(0));}

template<typename T> int count(const vector<T>& v, T t) {return count(v.begin(), v.end(), t);}

template<typename T, typename Function> int count_if(const vector<T>& v, Function func) {return count_if(v.begin(), v.end(), func);}

template<typename T, typename Function> void remove_if(vector<T>& v, Function func) {v.erase(remove_if(v.begin(), v.end(), func), v.end());}

template<typename T, typename Function> bool all_of(vector<T> v, Function func) {return all_of(v.begin(), v.end(), func);}

template<typename T, typename Function> bool any_of(vector<T> v, Function func) {return any_of(v.begin(), v.end(), func);}

template<typename T, typename Function> bool none_of(vector<T> v, Function func) {return none_of(v.begin(), v.end(), func);}

template<typename T> vector<T> subvector(vector<T>& v, int a, int b) {return vector<T>(v.begin() + a, v.begin() + b);}

template<typename T> int kinds(const vector<T>& v) {return set<T>(v.begin(), v.end()).size();}

template<typename T> map<T, int> count_kinds(const vector<T>& v) {
  map<T, int> res;
  for (const auto& i : v) ++res[i];
  return res;
}

template<typename T> void iota(vector<T>& v, T t = 0) {iota(v.begin(), v.end(), t);}

template<typename T> bool is_sorted(const vector<T>& v) {return is_sorted(v.begin(), v.end());}

int main() {
  int n, k, res = numeric_limits<int>::max();
  cin >> n >> k;
  vector<int> h(n);
  cin >> h;
  sort(h);
  for (int i = 0; i + k - 1 < n; ++i) chmin(res, h[i + k - 1] - h[i]);
  cout << res << endl;
}