Anastasia loves going for a walk in Central Uzhlyandian Park. But she became uninterested in simple walking, so she began to collect Uzhlyandian pebbles. At first, she decided to collect all the pebbles she could find in the park.

She has only two pockets. She can put at most k pebbles in each pocket at the same time. There are n different pebble types in the park, and there are wi pebbles of the i-th type. Anastasia is very responsible, so she never mixes pebbles of different types in same pocket. However, she can put different kinds of pebbles in different pockets at the same time. Unfortunately, she can't spend all her time collecting pebbles, so she can collect pebbles from the park only once a day.

Help her to find the minimum number of days needed to collect all the pebbles of Uzhlyandian Central Park, taking into consideration that Anastasia can't place pebbles of different types in same pocket.

Input

The first line contains two integers n and k (1 ≤ n ≤ 105, 1 ≤ k ≤ 109) — the number of different pebble types and number of pebbles Anastasia can place in one pocket.

The second line contains n integers w1, w2, ..., wn (1 ≤ wi ≤ 104) — number of pebbles of each type. 

Output

The only line of output contains one integer — the minimum number of days Anastasia needs to collect all the pebbles.

Examples

Input

3 2
2 3 4


Output

3


Input

5 4
3 1 8 9 7


Output

5

Note

In the first sample case, Anastasia can collect all pebbles of the first type on the first day, of second type — on the second day, and of third type — on the third day.

Optimal sequence of actions in the second sample case: 

  * In the first day Anastasia collects 8 pebbles of the third type. 
  * In the second day she collects 8 pebbles of the fourth type. 
  * In the third day she collects 3 pebbles of the first type and 1 pebble of the fourth type. 
  * In the fourth day she collects 7 pebbles of the fifth type. 
  * In the fifth day she collects 1 pebble of the second type. 

import java.util.*;
import java.io.*;

  public class TestClass{
    static ArrayList<Integer>[] al;
         static class Pair implements Comparator<Pair>{
  int a;
  int b;
  Pair(){

  }
  Pair(int a,int b){
    this.a=a;
    this.b=b;
  }
  public int compare(Pair p1,Pair p2){

    return p1.a-p2.a;
 }
}
  
   static InputReader sc = new InputReader(); 

   static int gcd(int a,int b){
    if(a==0){
      return b;
    }
    return gcd(b%a,a);
   }
   static int d;
    
   static boolean[] v;
   /* static void dfs(int src,int x,int y){
      v[src]=true;
     int  i=1;
     color[src]=x;
      for(int a :al[src]){
        if(v[a]) continue;
        if(i==x|| i==y){
          i++;
          if(i==x|| i==y){
          i++;
        }
        }
        color[a]=i;
        i++;
         
      }
      for(int a:al[src]){
        if(!v[a]){
          dfs(a,color[a],x);
        }
      }




    }
    */
    static long[] a;
    static long[] b;
    public static boolean possible(double mid,int n){
      double l=a[1]-b[1]*mid;
      double r=a[1]+b[1]*mid;
      for(int i=2;i<=n;i++){
        l=Math.max(l,a[i]-b[i]*mid);
        r=Math.min(r,a[i]+b[i]*mid);

      }
      if(l>r)return false;
      else  return true;
    }

public static boolean isvowel(char ch){
    if(ch=='a'||ch=='e'||ch=='i'||ch=='o'||ch=='u'){
        return true;
    }else{
        return false;
    }
}
    static long[] fac;
    static long[] inv;
    static long mod=(long)1e9+7;
    static int[] prime;
    static Integer[] ans;
    static int[] color;
    static  int count_red=0;
    static int size=0;
   

    public static void main(String[] args) throws IOException{
             long n=l();
             long m=l();
             long ans=0;
             for(int i=0;i<n;i++){
              long k=l();

              ans+=k/m;
              if(k%m>0){
                ans+=1;
              }
             
             }
             System.out.println(ans/2+ans%2);
             
              
      }
           
           

        

    
    /////////////////////////////////////////////////////////// shortcuts //////////////////////////////
      public static long modPow(long base, long exp, long mod) {
        base = base % mod;
        long result = 1;
        while (exp > 0) {
            if (exp % 2 == 1) {
                result = (result * base) % mod;
                exp--;
            } else {
                base = (base * base) % mod;
                exp = exp >> 1;
            }
 
        }
        return result;
    }
 
 
    public static void cal() {
        fac = new long[1000005];
        inv = new long[1000005];
        fac[0] = 1;
        inv[0] = 1;
        for (int i = 1; i <= 1000000; i++) {
            fac[i] = (fac[i - 1] * i) % mod;
            inv[i] = (inv[i - 1] * modPow(i, mod - 2, mod)) % mod;
        }
    }
 
   /* public static long ncr(int n, int r) {
        return (((fac[n] * inv[r]) % mod) * inv[n - r]) % mod;
    }
 */

      static int i() {
           
          return sc.nextInt();
        }
        static long l() throws IOException{
          return sc.nextLong();

        }
        static double d() throws IOException{
          return sc.nextDouble();
        }
        static String s() throws IOException{
          return sc.next();

        }
        static String sL() throws IOException{
          return sc.nextLine();
        }
       static void loop(int[] a) throws IOException{
          for(int j=0;j<a.length;j++){
              a[j]=i();
          }
        }
        static void eloop(int[] a) throws IOException{
          for(int i=1;i<=a.length;i++){
              a[i]=i();
          }
        }
        static void ploop(int[] a)throws IOException{
             for(int j=0;j<a.length;j++){
                System.out.println(a[j]);
             }

        }
        static void eploop(int[] a)throws IOException{
             for(int j=1;j<=a.length;j++){
                System.out.println(a[j]);
             }

        } 
  
        ////////////////////////////////////////////////////////////////////////////////////////////////////
     

   

  static class InputReader {
        BufferedReader br;
        StringTokenizer st;
 
        public InputReader() {
            br = new BufferedReader(new
                    InputStreamReader(System.in));
        }
 
        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                }
                catch (IOException  e) {
                    throw new RuntimeException();
                }
            }
            return st.nextToken();
        }
 
        int nextInt() {
            return Integer.parseInt(next());
        }
 
        long nextLong() {
            return Long.parseLong(next());
        }
 
        double nextDouble() {
            return Double.parseDouble(next());
        }
 
        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            }
            catch (IOException e) {
                throw new RuntimeException();
            }
            return str;
        }
    }

 }