There is a toy building consisting of n towers. Each tower consists of several cubes standing on each other. The i-th tower consists of h_i cubes, so it has height h_i.

Let's define operation slice on some height H as following: for each tower i, if its height is greater than H, then remove some top cubes to make tower's height equal to H. Cost of one "slice" equals to the total number of removed cubes from all towers.

Let's name slice as good one if its cost is lower or equal to k (k ≥ n).

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Calculate the minimum number of good slices you have to do to make all towers have the same height. Of course, it is always possible to make it so.

Input

The first line contains two integers n and k (1 ≤ n ≤ 2 ⋅ 10^5, n ≤ k ≤ 10^9) — the number of towers and the restriction on slices, respectively.

The second line contains n space separated integers h_1, h_2, ..., h_n (1 ≤ h_i ≤ 2 ⋅ 10^5) — the initial heights of towers.

Output

Print one integer — the minimum number of good slices you have to do to make all towers have the same heigth.

Examples

Input

5 5
3 1 2 2 4


Output

2


Input

4 5
2 3 4 5


Output

2

Note

In the first example it's optimal to make 2 slices. The first slice is on height 2 (its cost is 3), and the second one is on height 1 (its cost is 4).

import java.io.BufferedReader;
import java.io.BufferedWriter;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.lang.reflect.Array;
import java.util.Arrays;
import java.util.Comparator;
import java.util.StringTokenizer;
import java.util.function.Function;

public class P1065C {

    static boolean multipleIndependent = false;

    void run() {
        int n = in.nextInt();
        int k = in.nextInt();
        long[] H = in.nextLongArray(n);
        Arrays.sort(H);
        flip(H, 0, n - 1);
        long c = 0;
        long r = 0;
        for (int i = 1; i < n; i++) {
            H[i - 1] -= r / i;
            if (H[i - 1] <= H[i]) {
                r = r % i + (H[i] - H[i - 1]) * i;
            } else {
                c += (H[i - 1] - H[i] + k / i - 1) / (k / i);
                r = (H[i - 1] - H[i] + k / i - 1) / (k / i) * (k / i) - (H[i - 1] - H[i]);
                r *= i;
                r += k % i;
            }
//            System.out.println(c + " " + r);
        }
        out.println(c);
    }

    void flip(long[] arr, int l, int r) {
        while (l < r) {
            long tmp = arr[l];
            arr[l++] = arr[r];
            arr[r--] = tmp;
        }
    }

    /* -----: Template :----- */
    static InputReader in = new InputReader(System.in);
    static PrintWriter out = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));

    public static void main(String[] args) {
        int q = multipleIndependent ? in.nextInt() : 1;
        while (q-- > 0) {
            new P1065C().run();
        }
        out.flush();
        out.close();
    }

    static class InputReader {

        private final BufferedReader reader;
        private StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            int bufferSize = 32 * 1024;
            reader = new BufferedReader(new InputStreamReader(stream), bufferSize);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

        public long nextLong() {
            return Long.parseLong(next());
        }

        public int[] nextIntArray(int n) {
            int[] arr = new int[n];
            for (int i = 0; i < n; i++) {
                arr[i] = nextInt();
            }
            return arr;
        }

        public <T> T[] nextIntArrayWithFunction(int n, Function<Integer, T> function, Class<T> c) {
            T[] arr = (T[]) Array.newInstance(c, n);
            for (int i = 0; i < n; i++) {
                arr[i] = function.apply(nextInt());
            }
            return arr;
        }

        public long[] nextLongArray(int n) {
            long[] arr = new long[n];
            for (int i = 0; i < n; i++) {
                arr[i] = nextLong();
            }
            return arr;
        }

        public <T> T[] nextLongArrayWithFunction(int n, Function<Long, T> function, Class<T> c) {
            T[] arr = (T[]) Array.newInstance(c, n);
            for (int i = 0; i < n; i++) {
                arr[i] = function.apply(nextLong());
            }
            return arr;
        }

        public int[][] nextIntMap(int n, int m) {
            int[][] map = new int[n][m];
            for (int i = 0; i < n; i++) {
                map[i] = nextIntArray(m);
            }
            return map;
        }

        public long[][] nextLongMap(int n, int m) {
            long[][] map = new long[n][m];
            for (int i = 0; i < n; i++) {
                map[i] = nextLongArray(m);
            }
            return map;
        }

        public char[][] nextCharMap(int n) {
            char[][] map = new char[n][];
            for (int i = 0; i < n; i++) {
                map[i] = next().toCharArray();
            }
            return map;
        }
    }

    static int numLength(long n) {
        int l = 0;
        while (n > 0) {
            n /= 10;
            l++;
        }
        return l;
    }

    static <R> long binarySearch(long lowerBound, long upperBound,
            R value, Function<Long, R> generatorFunction, Comparator<R> comparator) {
        if (lowerBound <= upperBound) {
            long mid = (lowerBound + upperBound) / 2;
            int compare = comparator.compare(generatorFunction.apply(mid), value);
            if (compare == 0) {
                return mid;
            } else if (compare < 0) {
                return binarySearch(mid + 1, upperBound, value, generatorFunction, comparator);
            } else {
                return binarySearch(lowerBound, mid - 1, value, generatorFunction, comparator);
            }
        } else {
            return -1;
        }
    }

    static <T> Integer[] sortSimultaneously(T[] key, Comparator<T> comparator,
            Object[]... moreArrays) {
        int n = key.length;
        for (Object[] array : moreArrays) {
            if (array.length != n) {
                throw new RuntimeException("Arrays must have equals lengths");
            }
        }
        Integer[] indices = new Integer[n];
        for (int i = 0; i < n; i++) {
            indices[i] = i;
        }
        Comparator<Integer> delegatingComparator = (a, b) -> {
            return comparator.compare(key[a], key[b]);
        };
        Arrays.sort(indices, delegatingComparator);
        reorder(indices, key);
        for (Object[] array : moreArrays) {
            reorder(indices, array);
        }
        return indices;
    }

    static void reorder(Integer[] indices, Object[] arr) {
        if (indices.length != arr.length) {
            throw new RuntimeException("Arrays must have equals lengths");
        }
        int n = arr.length;
        Object[] copy = new Object[n];
        for (int i = 0; i < n; i++) {
            copy[i] = arr[indices[i]];
        }
        System.arraycopy(copy, 0, arr, 0, n);
    }

    static int prodMod(int a, int b, int mod) {
        return (int) (((long) a) * b % mod);
    }

    static long prodMod(long a, long b, long mod) {
        long res = 0;
        a %= mod;
        b %= mod;
        while (b > 0) {
            if ((b & 1) > 0) {
                res = (res + a) % mod;
            }
            a = (a << 1) % mod;
            b >>= 1;
        }
        return res;
    }

    static long sumMod(int[] b, long mod) {
        long res = 0;
        for (int i = 0; i < b.length; i++) {
            res = (res + b[i] % mod) % mod;
        }
        return res;
    }

    static long sumMod(long[] a, long mod) {
        long res = 0;
        for (int i = 0; i < a.length; i++) {
            res = (res + a[i] % mod) % mod;
        }
        return res;
    }

    static long sumProdMod(int[] a, long b, long mod) {
        long res = sumMod(a, mod);
        return prodMod(res, b, mod);
    }

    static long sumProdMod(long[] a, long b, long mod) {
        long res = sumMod(a, mod);
        return prodMod(res, b, mod);
    }

    static long sumProdMod(int[] a, int[] b, long mod) {
        if (a.length != b.length) {
            throw new RuntimeException("Arrays must have equals lengths");
        }
        long res = 0;
        for (int i = 0; i < a.length; i++) {
            res = (res + prodMod(a[i], b[i], mod)) % mod;
        }
        return res;
    }

    static long sumProdMod(long[] a, long[] b, long mod) {
        if (a.length != b.length) {
            throw new RuntimeException("Arrays must have equals lengths");
        }
        long res = 0;
        for (int i = 0; i < a.length; i++) {
            res = (res + prodMod(a[i], b[i], mod)) % mod;
        }
        return res;
    }

    static int[] toPrimitive(Integer[] arr) {
        int[] res = new int[arr.length];
        for (int i = 0; i < arr.length; i++) {
            res[i] = arr[i];
        }
        return res;
    }

    static int[][] toPrimitive(Integer[][] arr) {
        int[][] res = new int[arr.length][];
        for (int i = 0; i < arr.length; i++) {
            res[i] = toPrimitive(arr[i]);
        }
        return res;
    }

    static long[] toPrimitive(Long[] arr) {
        long[] res = new long[arr.length];
        for (int i = 0; i < arr.length; i++) {
            res[i] = arr[i];
        }
        return res;
    }

    static long[][] toPrimitive(Long[][] arr) {
        long[][] res = new long[arr.length][];
        for (int i = 0; i < arr.length; i++) {
            res[i] = toPrimitive(arr[i]);
        }
        return res;
    }

    static Integer[] toWrapper(int[] arr) {
        Integer[] res = new Integer[arr.length];
        for (int i = 0; i < arr.length; i++) {
            res[i] = arr[i];
        }
        return res;
    }

    static Integer[][] toWrapper(int[][] arr) {
        Integer[][] res = new Integer[arr.length][];
        for (int i = 0; i < arr.length; i++) {
            res[i] = toWrapper(arr[i]);
        }
        return res;
    }

    static Long[] toWrapper(long[] arr) {
        Long[] res = new Long[arr.length];
        for (int i = 0; i < arr.length; i++) {
            res[i] = arr[i];
        }
        return res;
    }

    static Long[][] toWrapper(long[][] arr) {
        Long[][] res = new Long[arr.length][];
        for (int i = 0; i < arr.length; i++) {
            res[i] = toWrapper(arr[i]);
        }
        return res;
    }
}
