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 (GCC 5.4.1) (judge verdict: Accepted)

#include <stdio.h>
#include <string.h>
#include <stdlib.h>
#include <time.h>
#define inf 1072114514
#define llinf 4154118101919364364
#define mod 1000000007
#define pi 3.1415926535897932384

int max(int a, int b)
{
  if (a > b)
  {
    return a;
  }
  return b;
}
int min(int a, int b)
{
  if (a < b)
  {
    return a;
  }
  return b;
}
int zt(int a, int b) { return max(a, b) - min(a, b); }
int round(int a, int b)
{
  if ((a % b) * 2 >= b)
  {
    return (a / b) + 1;
  }
  return a / b;
}
int ceil(int a, int b)
{
  if (a % b == 0)
  {
    return a / b;
  }
  return (a / b) + 1;
}
int gcd(int a, int b)
{
  int c;
  while (b != 0)
  {
    c = a % b;
    a = b;
    b = c;
  }
  return a;
}
int lcm(int a, int b)
{
  int c = gcd(a, b);
  a /= c;
  return a * b;
}
int nCr(int a, int b)
{
  int i, r = 1;
  for (i = 1; i <= b; i++)
  {
    r *= (a + 1 - i);
    r /= i;
  }
  return r;
}
int nHr(int a, int b) { return nCr(a + b - 1, b); }
int fact(int a)
{
  int i, r = 1;
  for (i = 1; i <= a; i++)
  {
    r *= i;
  }
  return r;
}
int pow(int a, int b)
{
  int i, r = 1;
  for (i = 1; i <= b; i++)
  {
    r *= a;
  }
  return r;
}
int dsum(int x)
{
  int r = 0;
  while (x)
  {
    r += (x % 10);
    x /= 10;
  }
  return r;
}
int dsumb(int x, int b)
{
  int r = 0;
  while (x)
  {
    r += (x % b);
    x /= b;
  }
  return r;
}
int sankaku(int x) { return ((1 + x) * x) / 2; }
long long llmax(long long a, long long b)
{
  if (a > b)
  {
    return a;
  }
  return b;
}
long long llmin(long long a, long long b)
{
  if (a < b)
  {
    return a;
  }
  return b;
}
long long llzt(long long a, long long b) { return llmax(a, b) - llmin(a, b); }
long long llround(long long a, long long b)
{
  if ((a % b) * 2 >= b)
  {
    return (a / b) + 1;
  }
  return a / b;
}
long long llceil(long long a, long long b)
{
  if (a % b == 0)
  {
    return a / b;
  }
  return (a / b) + 1;
}
long long llgcd(long long a, long long b)
{
  long long c;
  while (b != 0)
  {
    c = a % b;
    a = b;
    b = c;
  }
  return a;
}
long long lllcm(long long a, long long b)
{
  long long c = llgcd(a, b);
  a /= c;
  return a * b;
}
long long llnCr(long long a, long long b)
{
  long long i, r = 1;
  for (i = 1; i <= b; i++)
  {
    r *= (a + 1 - i);
    r /= i;
  }
  return r;
}
long long llnHr(long long a, long long b) { return llnCr(a + b - 1, b); }
long long llfact(long long a)
{
  long long i, r = 1;
  for (i = 1; i <= a; i++)
  {
    r *= i;
  }
  return r;
}
long long llpow(long long a, long long b)
{
  long long i, r = 1;
  for (i = 1; i <= b; i++)
  {
    r *= a;
  }
  return r;
}
long long lldsum(long long x)
{
  long long r = 0;
  while (x)
  {
    r += (x % 10);
    x /= 10;
  }
  return r;
}
long long lldsumb(long long x, long long b)
{
  long long r = 0;
  while (x)
  {
    r += (x % b);
    x /= b;
  }
  return r;
}
long long llsankaku(long long x) { return ((1 + x) * x) / 2; }
double dbmax(double a, double b)
{
  if (a > b)
  {
    return a;
  }
  return b;
}
double dbmin(double a, double b)
{
  if (a < b)
  {
    return a;
  }
  return b;
}
double dbzt(double a, double b) { return dbmax(a, b) - dbmin(a, b); }
int sortfncsj(const void *a, const void *b)
{
  if (*(int *)a > *(int *)b)
  {
    return 1;
  }
  if (*(int *)a == *(int *)b)
  {
    return 0;
  }
  return -1;
}
int sortfnckj(const void *a, const void *b)
{
  if (*(int *)a < *(int *)b)
  {
    return 1;
  }
  if (*(int *)a == *(int *)b)
  {
    return 0;
  }
  return -1;
}
int llsortfncsj(const void *a, const void *b)
{
  if (*(long long *)a > *(long long *)b)
  {
    return 1;
  }
  if (*(long long *)a == *(long long *)b)
  {
    return 0;
  }
  return -1;
}
int llsortfnckj(const void *a, const void *b)
{
  if (*(long long *)a < *(long long *)b)
  {
    return 1;
  }
  if (*(long long *)a == *(long long *)b)
  {
    return 0;
  }
  return -1;
}
int dbsortfncsj(const void *a, const void *b)
{
  if (*(double *)a > *(double *)b)
  {
    return 1;
  }
  if (*(double *)a == *(double *)b)
  {
    return 0;
  }
  return -1;
}
int dbsortfnckj(const void *a, const void *b)
{
  if (*(double *)a < *(double *)b)
  {
    return 1;
  }
  if (*(double *)a == *(double *)b)
  {
    return 0;
  }
  return -1;
}
int strsortfncsj(const void *a, const void *b) { return strcmp((char *)a, (char *)b); }
int strsortfnckj(const void *a, const void *b) { return strcmp((char *)b, (char *)a); }

void shuffledget(int x[], int n)
{
  srand(time(0));
  int i, b[524288], p, c;
  for (i = 0; i < n; i++)
  {
    b[i] = i;
  }
  for (i = n; i >= 1; i--)
  {
    p = rand() % i;
    c = b[i - 1];
    b[i - 1] = b[p];
    b[p] = c;
  }
  for (i = 0; i < n; i++)
  {
    scanf("%d", &x[b[i]]);
  }
}

int dx4[4] = {1, -1, 0, 0};
int dy4[4] = {0, 0, 1, -1};
int dx8[8] = {-1, -1, -1, 0, 0, 1, 1, 1};
int dy8[8] = {-1, 0, 1, -1, 1, -1, 0, 1};

int search(int x, int a[], int n)
{
  int st = 0, fi = n - 1, te;
  while (st <= fi)
  {
    te = (st + fi) / 2;
    if (a[te] < x)
    {
      st = te + 1;
    }
    else
    {
      fi = te - 1;
    }
  }
  return st;
}

typedef struct
{
  int val;
  int node;
} sd;

int sdsortfnc(const void *a, const void *b)
{
  if (((sd *)a)->val < ((sd *)b)->val)
  {
    return -1;
  }
  if (((sd *)a)->val > ((sd *)b)->val)
  {
    return 1;
  }
  return 0;
}

int main(void)
{
  int i, n, k, a[524288], r = inf;
  scanf("%d%d", &n, &k);
  for (i = 0; i < n; i++)
  {
    scanf("%d", &a[i]);
  }
  qsort(a, n, sizeof(int), sortfncsj);
  for (i = k - 1; i < n; i++)
  {
    r = min(r, a[i] - a[i - k + 1]);
  }
  printf("%d\n", r);
  return 0;
}